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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 8350.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 8350.f1 | 8350e1 | \([1, 0, 0, -651760518, -6404479935388]\) | \(-1224751130206834971784807336585/61328559574089728\) | \(-1533213989352243200\) | \([]\) | \(1537008\) | \(3.4117\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 8350.f1 has rank \(1\).
Complex multiplication
The elliptic curves in class 8350.f do not have complex multiplication.Modular form 8350.2.a.f
sage: E.q_eigenform(10)