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SageMath
sage: E = EllipticCurve("c1")
sage: E.isogeny_class()
Elliptic curves in class 4508.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4508.c1 | 4508a1 | \([0, 1, 0, 82, 2225]\) | \(32000/1127\) | \(-2121446768\) | \([]\) | \(1152\) | \(0.46954\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 4508.c1 has rank \(1\).
Complex multiplication
The elliptic curves in class 4508.c do not have complex multiplication.Modular form 4508.2.a.c
sage: E.q_eigenform(10)