Properties

Label 69360.cw
Number of curves 8
Conductor 69360
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("69360.cw1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 69360.cw

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
69360.cw1 69360du7 [0, 1, 0, -24662200, 47132459348] [2] 2654208  
69360.cw2 69360du8 [0, 1, 0, -2097080, 158390100] [2] 2654208  
69360.cw3 69360du6 [0, 1, 0, -1542200, 735243348] [2, 2] 1327104  
69360.cw4 69360du5 [0, 1, 0, -1334120, -593555532] [2] 884736  
69360.cw5 69360du4 [0, 1, 0, -316840, 59020340] [2] 884736  
69360.cw6 69360du2 [0, 1, 0, -85640, -8767500] [2, 2] 442368  
69360.cw7 69360du3 [0, 1, 0, -62520, 19670100] [2] 663552  
69360.cw8 69360du1 [0, 1, 0, 6840, -666252] [2] 221184 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 69360.cw have rank \(0\).

Modular form 69360.2.a.cw

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.