Show commands:
SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 32368.z
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 32368.z1 | 32368bj1 | \([0, 1, 0, -892528, 273546196]\) | \(2751936625/458752\) | \(13107784407341596672\) | \([]\) | \(470016\) | \(2.3895\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 32368.z1 has rank \(0\).
Complex multiplication
The elliptic curves in class 32368.z do not have complex multiplication.Modular form 32368.2.a.z
sage: E.q_eigenform(10)