Show commands:
SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 162288.w
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
162288.w1 | 162288j1 | \([0, 0, 0, 81835341, 503942130034]\) | \(503009937352889/1201583849472\) | \(-144785116111393746831015936\) | \([]\) | \(50319360\) | \(3.7037\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 162288.w1 has rank \(1\).
Complex multiplication
The elliptic curves in class 162288.w do not have complex multiplication.Modular form 162288.2.a.w
sage: E.q_eigenform(10)