Show commands:
SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 5610.z
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
5610.z1 | 5610x1 | \([1, 1, 1, -5389351, 9273693149]\) | \(-17311437234395043487224049/27152400000000000000000\) | \(-27152400000000000000000\) | \([]\) | \(542640\) | \(2.9960\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 5610.z1 has rank \(0\).
Complex multiplication
The elliptic curves in class 5610.z do not have complex multiplication.Modular form 5610.2.a.z
sage: E.q_eigenform(10)