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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 458640.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
458640.f1 | 458640f1 | \([0, 0, 0, -37443, 3016258]\) | \(-39678209809/3900000\) | \(-570621542400000\) | \([]\) | \(1843200\) | \(1.5722\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 458640.f1 has rank \(1\).
Complex multiplication
The elliptic curves in class 458640.f do not have complex multiplication.Modular form 458640.2.a.f
sage: E.q_eigenform(10)