Show commands:
SageMath
E = EllipticCurve("bn1")
E.isogeny_class()
Elliptic curves in class 205350.bn
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
205350.bn1 | 205350da1 | \([1, 0, 1, 50624, -17019352]\) | \(357911/3330\) | \(-133497952218281250\) | \([]\) | \(2626560\) | \(1.9673\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 205350.bn1 has rank \(2\).
Complex multiplication
The elliptic curves in class 205350.bn do not have complex multiplication.Modular form 205350.2.a.bn
sage: E.q_eigenform(10)