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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 1215.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
1215.c1 | 1215i1 | \([1, -1, 1, -2, 4]\) | \(-2187/25\) | \(-6075\) | \([]\) | \(72\) | \(-0.59206\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 1215.c1 has rank \(1\).
Complex multiplication
The elliptic curves in class 1215.c do not have complex multiplication.Modular form 1215.2.a.c
sage: E.q_eigenform(10)