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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 997b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
997.c1 | 997b1 | \([0, -1, 1, -5, -3]\) | \(16777216/997\) | \(997\) | \([]\) | \(48\) | \(-0.67163\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 997b1 has rank \(2\).
Complex multiplication
The elliptic curves in class 997b do not have complex multiplication.Modular form 997.2.a.b
sage: E.q_eigenform(10)