Properties

Label 162624gq
Number of curves $1$
Conductor $162624$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("gq1")
 
E.isogeny_class()
 

Elliptic curves in class 162624gq

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
162624.in1 162624gq1 \([0, 1, 0, 191, 5663]\) \(24167/441\) \(-13988265984\) \([]\) \(147456\) \(0.62724\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 162624gq1 has rank \(1\).

Complex multiplication

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

Modular form 162624.2.a.gq

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