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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 5056.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
5056.f1 | 5056s1 | \([0, -1, 0, -721, 7697]\) | \(2533446736/79\) | \(1294336\) | \([]\) | \(1152\) | \(0.26926\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 5056.f1 has rank \(1\).
Complex multiplication
The elliptic curves in class 5056.f do not have complex multiplication.Modular form 5056.2.a.f
sage: E.q_eigenform(10)