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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 12584c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
12584.g1 | 12584c1 | \([0, 1, 0, -1976, 34736]\) | \(-235298/13\) | \(-47166040064\) | \([]\) | \(11200\) | \(0.80592\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 12584c1 has rank \(1\).
Complex multiplication
The elliptic curves in class 12584c do not have complex multiplication.Modular form 12584.2.a.c
sage: E.q_eigenform(10)