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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 4200.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
4200.f1 | 4200i1 | \([0, -1, 0, -708, 8037]\) | \(-6288640/567\) | \(-3543750000\) | \([]\) | \(1920\) | \(0.57556\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 4200.f1 has rank \(1\).
Complex multiplication
The elliptic curves in class 4200.f do not have complex multiplication.Modular form 4200.2.a.f
sage: E.q_eigenform(10)