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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 279174c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
279174.c1 | 279174c1 | \([1, 1, 0, -469401, -510709275]\) | \(-39578501433808712953/366679396931428224\) | \(-105970345713182756736\) | \([]\) | \(10692864\) | \(2.5249\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 279174c1 has rank \(1\).
Complex multiplication
The elliptic curves in class 279174c do not have complex multiplication.Modular form 279174.2.a.c
sage: E.q_eigenform(10)