Show commands:
SageMath
E = EllipticCurve("gc1")
E.isogeny_class()
Elliptic curves in class 76050.gc
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
76050.gc1 | 76050fz1 | \([1, -1, 1, 18220, -10455753]\) | \(304175/21632\) | \(-47573415648720000\) | \([]\) | \(846720\) | \(1.8796\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 76050.gc1 has rank \(0\).
Complex multiplication
The elliptic curves in class 76050.gc do not have complex multiplication.Modular form 76050.2.a.gc
sage: E.q_eigenform(10)