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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 50025r
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
50025.s1 | 50025r1 | \([0, 1, 1, -1283, -18031]\) | \(14959673344/90045\) | \(1406953125\) | \([]\) | \(39168\) | \(0.59468\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 50025r1 has rank \(1\).
Complex multiplication
The elliptic curves in class 50025r do not have complex multiplication.Modular form 50025.2.a.r
sage: E.q_eigenform(10)