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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 8619f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
8619.m1 | 8619f1 | \([0, -1, 1, -56, -271]\) | \(-692224/867\) | \(-24762387\) | \([]\) | \(5232\) | \(0.11211\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 8619f1 has rank \(0\).
Complex multiplication
The elliptic curves in class 8619f do not have complex multiplication.Modular form 8619.2.a.f
sage: E.q_eigenform(10)