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SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 338100.z
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 338100.z1 | 338100z1 | \([0, -1, 0, -15174483333, -719475395900463]\) | \(-1313824034189516800000/59606972523\) | \(-17531751775896067500000000\) | \([]\) | \(279936000\) | \(4.3244\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 338100.z1 has rank \(0\).
Complex multiplication
The elliptic curves in class 338100.z do not have complex multiplication.Modular form 338100.2.a.z
sage: E.q_eigenform(10)