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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 328560x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 328560.x1 | 328560x1 | \([0, -1, 0, -4019840, -197169451008]\) | \(-683565019129/1597684769280\) | \(-16790413335751753381969920\) | \([]\) | \(70917120\) | \(3.5192\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 328560x1 has rank \(1\).
Complex multiplication
The elliptic curves in class 328560x do not have complex multiplication.Modular form 328560.2.a.x
sage: E.q_eigenform(10)