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SageMath
E = EllipticCurve("b1")
E.isogeny_class()
Elliptic curves in class 12635.b
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
12635.b1 | 12635e1 | \([0, 0, 1, -6137, 184922]\) | \(196145197056/153125\) | \(19955403125\) | \([]\) | \(14400\) | \(0.90758\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 12635.b1 has rank \(1\).
Complex multiplication
The elliptic curves in class 12635.b do not have complex multiplication.Modular form 12635.2.a.b
sage: E.q_eigenform(10)