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SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 41650.bg
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
41650.bg1 | 41650w1 | \([1, -1, 0, -78997, -8655739]\) | \(-75659639517/1336336\) | \(-962963888642000\) | \([]\) | \(419328\) | \(1.6722\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 41650.bg1 has rank \(0\).
Complex multiplication
The elliptic curves in class 41650.bg do not have complex multiplication.Modular form 41650.2.a.bg
sage: E.q_eigenform(10)