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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 381150x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 381150.x1 | 381150x1 | \([1, -1, 0, -285863067, 1860388678341]\) | \(-15491003951990952121/75014100000\) | \(-12510112005857812500000\) | \([]\) | \(87091200\) | \(3.4406\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 381150x1 has rank \(1\).
Complex multiplication
The elliptic curves in class 381150x do not have complex multiplication.Modular form 381150.2.a.x
sage: E.q_eigenform(10)