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SageMath
E = EllipticCurve("ex1")
E.isogeny_class()
Elliptic curves in class 190575.ex
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 190575.ex1 | 190575fb1 | \([0, 0, 1, -898425, 234713531]\) | \(1216512/343\) | \(22612413565156078125\) | \([]\) | \(5322240\) | \(2.4207\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 190575.ex1 has rank \(1\).
Complex multiplication
The elliptic curves in class 190575.ex do not have complex multiplication.Modular form 190575.2.a.ex
sage: E.q_eigenform(10)