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SageMath
E = EllipticCurve("bc1")
E.isogeny_class()
Elliptic curves in class 355740bc
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
355740.bc1 | 355740bc1 | \([0, -1, 0, -24845, 1663257]\) | \(-630784/75\) | \(-201668835244800\) | \([]\) | \(1330560\) | \(1.4804\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 355740bc1 has rank \(1\).
Complex multiplication
The elliptic curves in class 355740bc do not have complex multiplication.Modular form 355740.2.a.bc
sage: E.q_eigenform(10)