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SageMath
E = EllipticCurve("a1")
E.isogeny_class()
Elliptic curves in class 2025.a
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
2025.a1 | 2025e1 | \([0, 0, 1, -675, 5906]\) | \(36864/5\) | \(4613203125\) | \([]\) | \(1728\) | \(0.58153\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 2025.a1 has rank \(1\).
Complex multiplication
The elliptic curves in class 2025.a do not have complex multiplication.Modular form 2025.2.a.a
sage: E.q_eigenform(10)