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SageMath
E = EllipticCurve("bd1")
E.isogeny_class()
Elliptic curves in class 8400bd
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
8400.cc1 | 8400bd1 | \([0, 1, 0, -708, -8037]\) | \(-6288640/567\) | \(-3543750000\) | \([]\) | \(3840\) | \(0.57556\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 8400bd1 has rank \(1\).
Complex multiplication
The elliptic curves in class 8400bd do not have complex multiplication.Modular form 8400.2.a.bd
sage: E.q_eigenform(10)