Properties

Label 116242.x
Number of curves $1$
Conductor $116242$
CM no
Rank $1$

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Show commands: SageMath
E = EllipticCurve("x1")
 
E.isogeny_class()
 

Elliptic curves in class 116242.x

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
116242.x1 116242q1 \([1, 0, 0, -409697644, -3187118709488]\) \(23568486981643074043/40748749519744\) \(13149120169899323265448576\) \([]\) \(38814720\) \(3.7139\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curve 116242.x1 has rank \(1\).

Complex multiplication

The elliptic curves in class 116242.x do not have complex multiplication.

Modular form 116242.2.a.x

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + 3 q^{5} + q^{6} - q^{7} + q^{8} - 2 q^{9} + 3 q^{10} - q^{11} + q^{12} - 2 q^{13} - q^{14} + 3 q^{15} + q^{16} - 2 q^{17} - 2 q^{18} + O(q^{20})\) Copy content Toggle raw display