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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 2100.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2100.c1 | 2100f1 | \([0, -1, 0, 42, -63]\) | \(800000/567\) | \(-5670000\) | \([]\) | \(288\) | \(-0.015651\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 2100.c1 has rank \(1\).
Complex multiplication
The elliptic curves in class 2100.c do not have complex multiplication.Modular form 2100.2.a.c
sage: E.q_eigenform(10)