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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 300042f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 300042.f1 | 300042f1 | \([1, -1, 0, -2016, -38768]\) | \(-1243337227777/194427216\) | \(-141737440464\) | \([]\) | \(397824\) | \(0.86837\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 300042f1 has rank \(1\).
Complex multiplication
The elliptic curves in class 300042f do not have complex multiplication.Modular form 300042.2.a.f
sage: E.q_eigenform(10)