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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 12789b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
12789.a1 | 12789b1 | \([0, 0, 1, -147, 9616]\) | \(-200704/22707\) | \(-39744720603\) | \([]\) | \(20160\) | \(0.71330\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 12789b1 has rank \(2\).
Complex multiplication
The elliptic curves in class 12789b do not have complex multiplication.Modular form 12789.2.a.b
sage: E.q_eigenform(10)