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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 6699.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
6699.b1 | 6699c1 | \([1, 1, 1, 0, -12]\) | \(-1/60291\) | \(-60291\) | \([]\) | \(432\) | \(-0.40387\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 6699.b1 has rank \(1\).
Complex multiplication
The elliptic curves in class 6699.b do not have complex multiplication.Modular form 6699.2.a.b
sage: E.q_eigenform(10)