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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 4864f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4864.n1 | 4864f1 | \([0, 1, 0, 3, -37]\) | \(64/19\) | \(-622592\) | \([]\) | \(512\) | \(-0.20904\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 4864f1 has rank \(0\).
Complex multiplication
The elliptic curves in class 4864f do not have complex multiplication.Modular form 4864.2.a.f
sage: E.q_eigenform(10)