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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 4008c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4008.b1 | 4008c1 | \([0, 1, 0, -296, -2064]\) | \(-1405190738/1503\) | \(-3078144\) | \([]\) | \(576\) | \(0.16131\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 4008c1 has rank \(1\).
Complex multiplication
The elliptic curves in class 4008c do not have complex multiplication.Modular form 4008.2.a.c
sage: E.q_eigenform(10)