Show commands:
SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 666.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
666.c1 | 666a1 | \([1, -1, 0, -231, -1315]\) | \(-69426531/1184\) | \(-23304672\) | \([]\) | \(240\) | \(0.21211\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 666.c1 has rank \(0\).
Complex multiplication
The elliptic curves in class 666.c do not have complex multiplication.Modular form 666.2.a.c
sage: E.q_eigenform(10)