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SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 40656bg
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
40656.p1 | 40656bg1 | \([0, -1, 0, -206466, -36041553]\) | \(-34339609640704/916839\) | \(-25987779450864\) | \([]\) | \(172800\) | \(1.6790\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 40656bg1 has rank \(1\).
Complex multiplication
The elliptic curves in class 40656bg do not have complex multiplication.Modular form 40656.2.a.bg
sage: E.q_eigenform(10)