Properties

Label 163254.q
Number of curves $1$
Conductor $163254$
CM no
Rank $2$

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

Elliptic curves in class 163254.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
163254.q1 163254df1 \([1, 1, 0, -192832, 32941888]\) \(-972115190761/14930496\) \(-12179264266967616\) \([]\) \(1857024\) \(1.8889\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 163254.q1 has rank \(2\).

Complex multiplication

The elliptic curves in class 163254.q do not have complex multiplication.

Modular form 163254.2.a.q

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{5} + q^{6} + q^{7} - q^{8} + q^{9} - q^{10} - q^{12} - q^{14} - q^{15} + q^{16} - 7 q^{17} - q^{18} - 2 q^{19} + O(q^{20})\) Copy content Toggle raw display