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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 4025.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4025.c1 | 4025g1 | \([0, -1, 1, -343, 2563]\) | \(-35806478336/3703\) | \(-462875\) | \([]\) | \(544\) | \(0.11961\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 4025.c1 has rank \(1\).
Complex multiplication
The elliptic curves in class 4025.c do not have complex multiplication.Modular form 4025.2.a.c
sage: E.q_eigenform(10)