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SageMath
E = EllipticCurve("f1")
E.isogeny_class()
Elliptic curves in class 2025.f
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 2025.f1 | 2025d1 | \([0, 0, 1, -75, -219]\) | \(36864/5\) | \(6328125\) | \([]\) | \(576\) | \(0.032222\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 2025.f1 has rank \(1\).
Complex multiplication
The elliptic curves in class 2025.f do not have complex multiplication.Modular form 2025.2.a.f
sage: E.q_eigenform(10)