Show commands:
SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 169338.z
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 169338.z1 | 169338e1 | \([1, 0, 0, -551535, 157835313]\) | \(-3843995587427449/6390046584\) | \(-30843534362070456\) | \([]\) | \(1935360\) | \(2.0599\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 169338.z1 has rank \(1\).
Complex multiplication
The elliptic curves in class 169338.z do not have complex multiplication.Modular form 169338.2.a.z
sage: E.q_eigenform(10)