Properties

Label 116242.k
Number of curves $2$
Conductor $116242$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("k1")
 
E.isogeny_class()
 

Elliptic curves in class 116242.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
116242.k1 116242k2 \([1, 1, 0, -689517, 219508205]\) \(770616005574241/2349948272\) \(110555386760667632\) \([2]\) \(3502080\) \(2.1389\)  
116242.k2 116242k1 \([1, 1, 0, -25277, 6287165]\) \(-37966934881/342216448\) \(-16099874288850688\) \([2]\) \(1751040\) \(1.7923\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 116242.k have rank \(1\).

Complex multiplication

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

Modular form 116242.2.a.k

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

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.