Show commands:
SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 54777c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
54777.b1 | 54777c1 | \([0, 1, 1, -2242, -45710]\) | \(-1404928/171\) | \(-151763129451\) | \([]\) | \(118560\) | \(0.88045\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 54777c1 has rank \(1\).
Complex multiplication
The elliptic curves in class 54777c do not have complex multiplication.Modular form 54777.2.a.c
sage: E.q_eigenform(10)