Properties

Label 162624.q
Number of curves $1$
Conductor $162624$
CM no
Rank $1$

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("q1")
 
E.isogeny_class()
 

Elliptic curves in class 162624.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
162624.q1 162624cl1 \([0, -1, 0, -44911489, 116948338465]\) \(-178284948703873/1944365472\) \(-109259523839218635767808\) \([]\) \(16727040\) \(3.2363\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 162624.q1 has rank \(1\).

Complex multiplication

The elliptic curves in class 162624.q do not have complex multiplication.

Modular form 162624.2.a.q

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