ADDENDA TO ELLIPTIC CURVE TABLES: N = 600 AND 702 Table 1: Elliptic Curve Data

The following table gives the data for the modular elliptic curves of conductor 702 which were omitted from the original Table 1. The format is the same as for the rest of Table 1.

a_{1} a_{2} a_{3}  a_{4}  a_{6} r |T| s ord(Δ) ord_{−}(j) c_{p} Kodaira Isogenies
702  N = 702 = 2 · 3^{3} · 13 (16 isogeny classes)  702
A1 1 −1 0  −9  −19 1 1 − 5, 3, 2 5, 0, 2 1, 1, 2 I_{5},II,I_{2} - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
B1 1 −1 0 −3 −1 1 1 + 1, 3, 1 1, 0, 1 1, 1, 1 I_{1},II,I_{1} - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
C1 1 −1 0 39 35 0 1 − 1, 11, 1 1, 0, 1 1, 1, 1 I_{1},II^{∗},I_{1} - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
D1 1 −1 0 −366 −2476 0 1 + 7, 11, 1 7, 0, 1 1, 1, 1 I_{7},II^{∗},I_{1} - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
E1 1 −1 0 −5826  173076 0 3 − 9, 3, 6 9, 0, 6 1, 1, 6 I_{9},II,I_{6} 3 : 2, 3
E2 1 −1 0 11919 881693 0 1 − 27, 9, 2 27, 0, 2 1, 1, 2 I_{27},IV^{∗},I_{2} 3 : 1
E3 1 −1 0 −472266 125037036 0 3 − 3, 5, 2 3, 0, 2 1, 3, 2 I_{3},IV,I_{2} 3 : 1 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
F1 1 −1 0 −648 9536 0 1 − 11, 3, 5 11, 0, 5 1, 1, 1 I_{11},II,I_{5} - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
G1 1 −1 0 −165 533 0 1 + 19, 3, 1 19, 0, 1 1, 1, 1 I_{19},II,I_{1} - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
H1 1 −1 0  −132  618 1 3 + 1, 3, 1 1, 0, 1 1, 1, 1 I_{1},II,I_{1} 3 : 2
H2 1 −1 0  −177  197 1 3 + 3, 9, 3 3, 0, 3 1, 3, 3 I_{3},IV^{∗},I_{3} 3 : 1, 3
H3 1 −1 0 −8952  −323776 1 1 + 9, 11, 1 9, 0, 1 1, 1, 1 I_{9},II^{∗},I_{1} 3 : 2 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
I1 1 −1 1 −29 55 0 1 + 1, 9, 1 1, 0, 1 1, 1, 1 I_{1},IV^{∗},I_{1} - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
J1 1 −1 1 −5834  −251639 0 1 − 11, 9, 5 11, 0, 5 11, 1, 1 I_{11},IV^{∗},I_{5} - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
K1 1 −1 1 −41 105 1 1 + 7, 5, 1 7, 0, 1 7, 3, 1 I_{7},IV,I_{1} - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
L1 1 −1 1 −83 595 1 1 − 5, 9, 2 5, 0, 2 5, 3, 2 I_{5},IV^{∗},I_{2} - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
M1 1 −1 1 −1487  −12905 1 1 + 19, 9, 1 19, 0, 1 19, 3, 1 I_{19},IV^{∗},I_{1} - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
N1 1 −1 1 −20 −1 0 3 + 3, 3, 3 3, 0, 3 3, 1, 3 I_{3},II,I_{3} 3 : 2, 3
N2 1 −1 1 −1190  −15497 0 1 + 1, 9, 1 1, 0, 1 1, 3, 1 I_{1},IV^{∗},I_{1} 3 : 1
N3 1 −1 1 −995 12323 0 3 + 9, 5, 1 9, 0, 1 9, 1, 1 I_{9},IV,I_{1} 3 : 1 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
O1 1 −1 1 4 −3 0 1 − 1, 5, 1 1, 0, 1 1, 1, 1 I_{1},IV,I_{1} - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
P1 1 −1 1 1324 −33097 0 3 − 27, 3, 2 27, 0, 2 27, 1, 2 I_{27},II,I_{2} 3 : 2
P2 1 −1 1 −52436 −4620617 0 3 − 9, 9, 6 9, 0, 6 9, 3, 6 I_{9},IV^{∗},I_{6} 3 : 1, 3
P3 1 −1 1 −4250396 −3371749577 0 1 − 3, 11, 2 3, 0, 2 3, 1, 2 I_{3},II^{∗},I_{2} 3 : 2

Table 2: Mordell–Weil generators

The following table gives the generators for the “strong Weil” curves of conductor 702 which were omitted from the original Table 2. The format is the same as for the rest of Table 2.

Curve  x  y
702 A  5  4
702 B  −1  1
702 H 7/2^{2} 151/2^{3}
702 K  −1  12
702 L  25  104
702M −29  86

Table 4: Birch–Swinnerton-Dyer data

The following table gives the Birch–Swinnerton-Dyer data for the “strong Weil” curves of conductor 600 and 702 which were omitted from the original Table 4. The format is the same as for the rest of Table 4.

Curve r  Ω  L^{(r)}(1)  R  L^{(r)}(1)/ΩR  S
600 E  1 1.6232936555 2.1589881844 0.0158333892 84.000000000 1.0
600 F  0 1.1134814845 1.1134814845 1.0  1  1
600G  0 0.7259589922 1.4519179844 1.0  2  1
600H  0 0.6100461910 1.8301385731 1.0  3  1
600 I  0 1.0159932080 2.0319864160 1.0  2  1

Curve r  Ω  L^{(r)}(1)  R  L^{(r)}(1)/ΩR  S
702 A  1 1.2959189179 1.6511976366 0.6370759828 2.0000000000 1.0
702 B  1 3.6218545346 1.5825343783 0.4369403473 1.0000000000 1.0
702 C  0 1.5516100045 1.5516100045 1.0000000000 1  1
702 D  0 1.0950637552 1.0950637552 1.0000000000 1  1
702 E  0 1.1045333203 0.7363555469 1.0000000000 2/3  1
702 F  0 1.1196604817 1.1196604817 1.0000000000 1  1
702 G  0 1.6442531135 1.6442531135 1.0000000000 1  1
702 H  1 4.4173331953 1.6516890684 3.3651981768 0.1111111111 1.0
702 I  0 2.7852340926 2.7852340926 1.0000000000 1  1
702 J  0 0.2651042420 2.9161466624 1.0000000000 11  1
702 K  1 2.9521289967 2.6395534641 0.0425770765 21.000000000 1.0
702 L  1 1.6844372293 2.6868354521 0.0531697947 30.000000000 1.0
702M  1 0.7927472332 2.6131420167 0.0578300306 57.000000000 1.0
702 N  0 2.4387240231 2.4387240231 1.0000000000 1  1
702 O  0 2.3848948730 2.3848948730 1.0000000000 1  1
702 P  0 0.4731564099 2.8389384593 1.0000000000 6  1

Table 3: Hecke eigenvalues

This table gives the Hecke eigenvalues for the 16 rational newforms at level 702 which were omitted from the original Table 3. Also the correct values for 100A, which were wrongly given originally. The format is the same as for the rest of Table 3.

2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 W_{q}
100 A (A) − 2 + −2 0 −2 6 −4 −6 6 −4 −2 6 10 6 6 12 2 −2 −12 −2 8 −6 −6 −2
702 A  + + 1 −5 5 + −6 −6 4 −2 1 −6 −12 4 2 −3 4 −14 −8 2 −13 8 −15 0 −7
702 B  + + −2 1 −1 + 0 0 −5 1 −5 −3 −6 1 −4 3 −11 4 −8 8 −16 8 −9 9 −4
702 C  + + 2 4 2 − −4 7 0 −9 −10 7 5 −2 −1 14 −8 10 −4 1 −4 −7 0 17 −8
702 D  + + 2 −5 −1 − 8 4 9 3 −7 7 2 1 8 −7 −11 4 8 −8 8 −4 15 −7 −8
702 E  + + −3 −1 −3 − 6 2 0 6 5 2 0 8 −6 9 12 −10 −4 6 11 8 −15 12 17
702 F  + − −2 4 2 + 0 −3 4 1 10 −3 9 10 11 −6 −8 −2 4 5 8 −7 12 −3 −16
702 G  + − 4 1 5 + 6 −6 −5 −5 −5 −9 6 7 −4 9 −5 −2 4 2 14 2 9 −3 14
702 H  + − 0 −1 −3 − −6 2 −3 −3 5 −7 6 −1 0 −9 3 −10 −4 −6 2 −10 9 −3 −10
702 I  − + 2 1 1 + 0 0 5 −1 −5 −3 6 1 4 −3 11 4 −8 −8 −16 8 9 −9 −4
702 J  − + 2 4 −2 + 0 −3 −4 −1 10 −3 −9 10 −11 6 8 −2 4 −5 8 −7 −12 3 −16
702 K  − + −2 −5 1 − −8 4 −9 −3 −7 7 −2 1 −8 7 11 4 8 8 8 −4 −15 7 −8
702 L  − − −1 −5 −5 + 6 −6 −4 2 1 −6 12 4 −2 3 −4 −14 −8 −2 −13 8 15 0 −7
702M  − − −4 1 −5 + −6 −6 5 5 −5 −9 −6 7 4 −9 5 −2 4 −2 14 2 −9 3 14
702 N  − − 0 −1 3 − 6 2 3 3 5 −7 −6 −1 0 9 −3 −10 −4 6 2 −10 −9 3 −10
702 O  − − −2 4 −2 − 4 7 0 9 −10 7 −5 −2 1 −14 8 10 −4 −1 −4 −7 0 −17 −8
702 P  − − 3 −1 3 − −6 2 0 −6 5 2 0 8 6 −9 −12 −10 −4 −6 11 8 15 −12 17