Properties

Label 55545.k
Number of curves $1$
Conductor $55545$
CM no
Rank $1$

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("k1")
 
E.isogeny_class()
 

Elliptic curves in class 55545.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
55545.k1 55545d1 \([0, -1, 1, -9887715, -11905786114]\) \(2580674412544/14467005\) \(599317544860416151245\) \([]\) \(2472960\) \(2.8291\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 55545.k1 has rank \(1\).

Complex multiplication

The elliptic curves in class 55545.k do not have complex multiplication.

Modular form 55545.2.a.k

sage: E.q_eigenform(10)
 
\(q - q^{3} - 2 q^{4} + q^{5} - q^{7} + q^{9} - 3 q^{11} + 2 q^{12} - 6 q^{13} - q^{15} + 4 q^{16} - 4 q^{17} - q^{19} + O(q^{20})\) Copy content Toggle raw display