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SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 257754.bg
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
257754.bg1 | 257754bg1 | \([1, 0, 1, -795652, 279866498]\) | \(-1184052061112257/34349180544\) | \(-1615987460320539264\) | \([]\) | \(5503680\) | \(2.2731\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 257754.bg1 has rank \(1\).
Complex multiplication
The elliptic curves in class 257754.bg do not have complex multiplication.Modular form 257754.2.a.bg
sage: E.q_eigenform(10)