Properties

Label 242760.cr
Number of curves $6$
Conductor $242760$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("242760.cr1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 242760.cr

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
242760.cr1 242760cr6 [0, 1, 0, -3028816, -2029849696] [2] 5242880  
242760.cr2 242760cr4 [0, 1, 0, -196616, -29183616] [2, 2] 2621440  
242760.cr3 242760cr2 [0, 1, 0, -52116, 4109184] [2, 2] 1310720  
242760.cr4 242760cr1 [0, 1, 0, -50671, 4373330] [2] 655360 \(\Gamma_0(N)\)-optimal
242760.cr5 242760cr3 [0, 1, 0, 69264, 20519760] [2] 2621440  
242760.cr6 242760cr5 [0, 1, 0, 323584, -156944736] [2] 5242880  

Rank

sage: E.rank()
 

The elliptic curves in class 242760.cr have rank \(0\).

Modular form 242760.2.a.cr

sage: E.q_eigenform(10)
 
\( q + q^{3} - q^{5} + q^{7} + q^{9} + 4q^{11} - 2q^{13} - q^{15} - 4q^{19} + O(q^{20}) \)

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 LMFDB numbering.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 8 & 4 \\ 2 & 1 & 2 & 4 & 4 & 2 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 8 & 4 & 2 & 1 & 4 & 8 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 2 & 4 & 8 & 8 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.