Show commands:
SageMath
E = EllipticCurve("z1")
E.isogeny_class()
Elliptic curves in class 230640.z
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
230640.z1 | 230640z1 | \([0, -1, 0, -230960, 46483392]\) | \(-360187951921/37500000\) | \(-141852825600000000\) | \([]\) | \(3456000\) | \(2.0303\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 230640.z1 has rank \(1\).
Complex multiplication
The elliptic curves in class 230640.z do not have complex multiplication.Modular form 230640.2.a.z
sage: E.q_eigenform(10)