Show commands:
SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 409101.z
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
409101.z1 | 409101z1 | \([0, -1, 1, -4869685, 4187113545]\) | \(-134217728/1863\) | \(-177267606758806387131\) | \([]\) | \(10881024\) | \(2.6916\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 409101.z1 has rank \(1\).
Complex multiplication
The elliptic curves in class 409101.z do not have complex multiplication.Modular form 409101.2.a.z
sage: E.q_eigenform(10)