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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 4641f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4641.a1 | 4641f1 | \([0, 1, 1, -14, -310]\) | \(-325660672/40000779\) | \(-40000779\) | \([]\) | \(2208\) | \(0.13816\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 4641f1 has rank \(1\).
Complex multiplication
The elliptic curves in class 4641f do not have complex multiplication.Modular form 4641.2.a.f
sage: E.q_eigenform(10)