Magma V2.21-9 Fri Mar 11 2016 08:13:49 on lehner [Seed = 3295823741]
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The modular curve X_0(20) is the elliptic curve Elliptic Curve defined by y^2 =
x^3 + x^2 + 4*x + 4 over Rational Field
with Cremona label 20a1
Points on X_0(20) over Q(zeta_7)^+ are [ (0 : 1 : 0), (4 : 10 : 1), (0 : 2 : 1),
(-1 : 0 : 1), (0 : -2 : 1), (4 : -10 : 1) ]
The cusps of X_0(20) are [
Place at (4 : 10 : 1),
Place at (4 : -10 : 1),
Place at (-1 : 0 : 1),
Place at (0 : -2 : 1),
Place at (0 : 2 : 1),
Place at (0 : 1 : 0)
]
Thus every Q(zeta_7)^+ point on X_0(20) is a cusp.
The modular curve X_0(11) is the elliptic curve Elliptic Curve defined by y^2 +
y = x^3 - x^2 - 10*x - 20 over Rational Field
with Cremona label 11a1
Points on X_0(11) over Q(zeta_7)^+ are [ (0 : 1 : 0), (5 : -6 : 1), (16 : 60 :
1), (16 : -61 : 1), (5 : 5 : 1) ]
The cusps of X_0(11) are [
Place at (16 : 60 : 1),
Place at (0 : 1 : 0)
]
The non-cuspidal points on X_0(11) over Q(zeta_7)^+ are [ (5 : -6 : 1), (16 :
-61 : 1), (5 : 5 : 1) ]
These have j-invariants [
-32768,
-121,
-24729001
]
Total time: 8.000 seconds, Total memory usage: 56.06MB