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SageMath
E = EllipticCurve("bf1")
E.isogeny_class()
Elliptic curves in class 80688bf
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
80688.v1 | 80688bf1 | \([0, 1, 0, 17931, -47646513]\) | \(524288/807003\) | \(-981337183436729088\) | \([]\) | \(1451520\) | \(2.1313\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 80688bf1 has rank \(1\).
Complex multiplication
The elliptic curves in class 80688bf do not have complex multiplication.Modular form 80688.2.a.bf
sage: E.q_eigenform(10)