Show commands:
SageMath
E = EllipticCurve("q1")
E.isogeny_class()
Elliptic curves in class 135240.q
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 135240.q1 | 135240du1 | \([0, -1, 0, 161439, 31372965]\) | \(315298651136/471571875\) | \(-695940612242400000\) | \([]\) | \(2096640\) | \(2.1091\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 135240.q1 has rank \(0\).
Complex multiplication
The elliptic curves in class 135240.q do not have complex multiplication.Modular form 135240.2.a.q
sage: E.q_eigenform(10)