Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("262080.im1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 262080im

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
262080.im7 262080im1 [0, 0, 0, -14817612, 21836400784] [2] 14155776 \(\Gamma_0(N)\)-optimal
262080.im6 262080im2 [0, 0, 0, -23849292, -7928403824] [2, 2] 28311552  
262080.im5 262080im3 [0, 0, 0, -91540812, -322423500656] [2] 42467328  
262080.im8 262080im4 [0, 0, 0, 93723828, -62905594736] [2] 56623104  
262080.im4 262080im5 [0, 0, 0, -285929292, -1857898707824] [2] 56623104  
262080.im2 262080im6 [0, 0, 0, -1446857292, -21182912634224] [2, 2] 84934656  
262080.im3 262080im7 [0, 0, 0, -1429076172, -21728928154736] [2] 169869312  
262080.im1 262080im8 [0, 0, 0, -23149702092, -1355708201662064] [2] 169869312  

Rank

sage: E.rank()
 

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

Modular form 262080.2.a.im

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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.