Properties

Label 114240jq
Number of curves 4
Conductor 114240
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("114240.ji1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 114240jq

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
114240.ji4 114240jq1 [0, 1, 0, 895, -17025] [2] 131072 \(\Gamma_0(N)\)-optimal
114240.ji3 114240jq2 [0, 1, 0, -7105, -191425] [2, 2] 262144  
114240.ji2 114240jq3 [0, 1, 0, -34305, 2262015] [2] 524288  
114240.ji1 114240jq4 [0, 1, 0, -107905, -13678465] [2] 524288  

Rank

sage: E.rank()
 

The elliptic curves in class 114240jq have rank \(0\).

Modular form 114240.2.a.ji

sage: E.q_eigenform(10)
 
\( q + q^{3} + q^{5} - q^{7} + q^{9} + 6q^{13} + q^{15} - q^{17} + 4q^{19} + O(q^{20}) \)

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 Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.