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SageMath
E = EllipticCurve("c1")
E.isogeny_class()
Elliptic curves in class 8619.c
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
8619.c1 | 8619l1 | \([0, 1, 1, -4, 4]\) | \(-53248/51\) | \(-8619\) | \([]\) | \(912\) | \(-0.54865\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 8619.c1 has rank \(1\).
Complex multiplication
The elliptic curves in class 8619.c do not have complex multiplication.Modular form 8619.2.a.c
sage: E.q_eigenform(10)