Show commands:
SageMath
E = EllipticCurve("bn1")
E.isogeny_class()
Elliptic curves in class 40656bn
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
40656.d1 | 40656bn1 | \([0, -1, 0, -18432, -1327104]\) | \(-1397395501513/740710656\) | \(-367108052484096\) | \([]\) | \(184320\) | \(1.4988\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curve 40656bn1 has rank \(1\).
Complex multiplication
The elliptic curves in class 40656bn do not have complex multiplication.Modular form 40656.2.a.bn
sage: E.q_eigenform(10)