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SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 72128bg
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
72128.u1 | 72128bg1 | \([0, -1, 0, 1111, -123647]\) | \(1257728/55223\) | \(-6652857064448\) | \([]\) | \(73728\) | \(1.1403\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 72128bg1 has rank \(1\).
Complex multiplication
The elliptic curves in class 72128bg do not have complex multiplication.Modular form 72128.2.a.bg
sage: E.q_eigenform(10)