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SageMath
E = EllipticCurve("u1")
E.isogeny_class()
Elliptic curves in class 49725u
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
49725.z1 | 49725u1 | \([0, 0, 1, 11625, 369531]\) | \(122023936/112047\) | \(-159535669921875\) | \([]\) | \(241920\) | \(1.4126\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 49725u1 has rank \(1\).
Complex multiplication
The elliptic curves in class 49725u do not have complex multiplication.Modular form 49725.2.a.u
sage: E.q_eigenform(10)