Show commands:
SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 189618.bg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 189618.bg1 | 189618u1 | \([1, 1, 1, -61293177, 194298623943]\) | \(-5275941807135921123097/326485867713527808\) | \(-1575884924652465445404672\) | \([]\) | \(39325440\) | \(3.3974\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 189618.bg1 has rank \(1\).
Complex multiplication
The elliptic curves in class 189618.bg do not have complex multiplication.Modular form 189618.2.a.bg
sage: E.q_eigenform(10)