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SageMath
E = EllipticCurve("h1")
E.isogeny_class()
Elliptic curves in class 5025.h
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
5025.h1 | 5025b1 | \([1, 1, 0, -25, 250]\) | \(-117649/1809\) | \(-28265625\) | \([]\) | \(1680\) | \(0.11113\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 5025.h1 has rank \(1\).
Complex multiplication
The elliptic curves in class 5025.h do not have complex multiplication.Modular form 5025.2.a.h
sage: E.q_eigenform(10)