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SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 41650bg
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
41650.a1 | 41650bg1 | \([1, -1, 0, -1612, 25696]\) | \(-75659639517/1336336\) | \(-8185058000\) | \([]\) | \(59904\) | \(0.69925\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 41650bg1 has rank \(2\).
Complex multiplication
The elliptic curves in class 41650bg do not have complex multiplication.Modular form 41650.2.a.bg
sage: E.q_eigenform(10)