Show commands:
SageMath
E = EllipticCurve("cj1")
E.isogeny_class()
Elliptic curves in class 416955cj
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
416955.cj1 | 416955cj1 | \([0, -1, 1, -45606, -3745753]\) | \(-222985990144/841995\) | \(-39612396572595\) | \([]\) | \(2122848\) | \(1.4686\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 416955cj1 has rank \(1\).
Complex multiplication
The elliptic curves in class 416955cj do not have complex multiplication.Modular form 416955.2.a.cj
sage: E.q_eigenform(10)