Properties

Label 169065.q
Number of curves $1$
Conductor $169065$
CM no
Rank $1$

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

Elliptic curves in class 169065.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
169065.q1 169065q1 \([0, 0, 1, -2086002, 1876221885]\) \(-1540318675894272/1442042265625\) \(-939799656560873671875\) \([]\) \(6128640\) \(2.7208\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 169065.q1 has rank \(1\).

Complex multiplication

The elliptic curves in class 169065.q do not have complex multiplication.

Modular form 169065.2.a.q

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