Properties

Label 32192.q
Number of curves $1$
Conductor $32192$
CM no
Rank $2$

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

Elliptic curves in class 32192.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
32192.q1 32192i1 \([0, 1, 0, -129, -673]\) \(-3650692/503\) \(-32964608\) \([]\) \(5120\) \(0.17434\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 32192.q1 has rank \(2\).

Complex multiplication

The elliptic curves in class 32192.q do not have complex multiplication.

Modular form 32192.2.a.q

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