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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 13005f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
13005.f1 | 13005f1 | \([1, -1, 1, 2113, 24786]\) | \(462866157/390625\) | \(-880885546875\) | \([]\) | \(16128\) | \(0.97967\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 13005f1 has rank \(1\).
Complex multiplication
The elliptic curves in class 13005f do not have complex multiplication.Modular form 13005.2.a.f
sage: E.q_eigenform(10)