Show commands:
SageMath
E = EllipticCurve("bn1")
E.isogeny_class()
Elliptic curves in class 25872bn
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
25872.i1 | 25872bn1 | \([0, -1, 0, -44, -132]\) | \(-768208/297\) | \(-3725568\) | \([]\) | \(3456\) | \(-0.029732\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 25872bn1 has rank \(1\).
Complex multiplication
The elliptic curves in class 25872bn do not have complex multiplication.Modular form 25872.2.a.bn
sage: E.q_eigenform(10)