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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 1002.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1002.c1 | 1002c1 | \([1, 0, 1, -3264, 71590]\) | \(-3843995587427449/6390046584\) | \(-6390046584\) | \([]\) | \(1008\) | \(0.77740\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 1002.c1 has rank \(1\).
Complex multiplication
The elliptic curves in class 1002.c do not have complex multiplication.Modular form 1002.2.a.c
sage: E.q_eigenform(10)