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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 12696.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
12696.b1 | 12696h1 | \([0, -1, 0, 8, 316]\) | \(92/81\) | \(-43877376\) | \([]\) | \(3840\) | \(0.14543\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 12696.b1 has rank \(2\).
Complex multiplication
The elliptic curves in class 12696.b do not have complex multiplication.Modular form 12696.2.a.b
sage: E.q_eigenform(10)