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SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 8400bg
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
8400.h1 | 8400bg1 | \([0, -1, 0, 1042, 5787]\) | \(800000/567\) | \(-88593750000\) | \([]\) | \(5760\) | \(0.78907\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 8400bg1 has rank \(0\).
Complex multiplication
The elliptic curves in class 8400bg do not have complex multiplication.Modular form 8400.2.a.bg
sage: E.q_eigenform(10)