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SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 42350bg
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
42350.t1 | 42350bg1 | \([1, -1, 0, -12062, 1730196]\) | \(-7243533/43904\) | \(-1176401538928000\) | \([]\) | \(133056\) | \(1.5755\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 42350bg1 has rank \(1\).
Complex multiplication
The elliptic curves in class 42350bg do not have complex multiplication.Modular form 42350.2.a.bg
sage: E.q_eigenform(10)