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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 12635j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
12635.a1 | 12635j1 | \([0, 1, 1, -120, -126]\) | \(533794816/300125\) | \(108345125\) | \([]\) | \(6912\) | \(0.23186\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 12635j1 has rank \(2\).
Complex multiplication
The elliptic curves in class 12635j do not have complex multiplication.Modular form 12635.2.a.j
sage: E.q_eigenform(10)