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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 2415c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2415.f1 | 2415c1 | \([0, 1, 1, 29169, -4304725]\) | \(2744564518708084736/9629735831296875\) | \(-9629735831296875\) | \([]\) | \(9360\) | \(1.7499\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 2415c1 has rank \(1\).
Complex multiplication
The elliptic curves in class 2415c do not have complex multiplication.Modular form 2415.2.a.c
sage: E.q_eigenform(10)