Properties

Label 262080.ll
Number of curves 8
Conductor 262080
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("262080.ll1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 262080.ll

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
262080.ll1 262080ll7 [0, 0, 0, -23149702092, 1355708201662064] [2] 169869312  
262080.ll2 262080ll6 [0, 0, 0, -1446857292, 21182912634224] [2, 2] 84934656  
262080.ll3 262080ll8 [0, 0, 0, -1429076172, 21728928154736] [2] 169869312  
262080.ll4 262080ll4 [0, 0, 0, -285929292, 1857898707824] [2] 56623104  
262080.ll5 262080ll3 [0, 0, 0, -91540812, 322423500656] [2] 42467328  
262080.ll6 262080ll2 [0, 0, 0, -23849292, 7928403824] [2, 2] 28311552  
262080.ll7 262080ll1 [0, 0, 0, -14817612, -21836400784] [2] 14155776 \(\Gamma_0(N)\)-optimal
262080.ll8 262080ll5 [0, 0, 0, 93723828, 62905594736] [2] 56623104  

Rank

sage: E.rank()
 

The elliptic curves in class 262080.ll have rank \(0\).

Modular form 262080.2.a.ll

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

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 LMFDB numbering.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 3 & 4 & 6 & 12 & 12 \\ 2 & 1 & 2 & 6 & 2 & 3 & 6 & 6 \\ 4 & 2 & 1 & 12 & 4 & 6 & 12 & 3 \\ 3 & 6 & 12 & 1 & 12 & 2 & 4 & 4 \\ 4 & 2 & 4 & 12 & 1 & 6 & 3 & 12 \\ 6 & 3 & 6 & 2 & 6 & 1 & 2 & 2 \\ 12 & 6 & 12 & 4 & 3 & 2 & 1 & 4 \\ 12 & 6 & 3 & 4 & 12 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.