Properties

Label 176610.cy
Number of curves 8
Conductor 176610
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("176610.cy1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 176610.cy

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
176610.cy1 176610u8 [1, 1, 1, -295386550, -1954166401165] [2] 27869184  
176610.cy2 176610u6 [1, 1, 1, -18462070, -30538193293] [2, 2] 13934592  
176610.cy3 176610u7 [1, 1, 1, -17116470, -35176745613] [2] 27869184  
176610.cy4 176610u5 [1, 1, 1, -3664675, -2654284915] [2] 9289728  
176610.cy5 176610u3 [1, 1, 1, -1238390, -403642765] [2] 6967296  
176610.cy6 176610u2 [1, 1, 1, -485695, 68193557] [2, 2] 4644864  
176610.cy7 176610u1 [1, 1, 1, -418415, 103959605] [2] 2322432 \(\Gamma_0(N)\)-optimal
176610.cy8 176610u4 [1, 1, 1, 1616805, 502990557] [2] 9289728  

Rank

sage: E.rank()
 

The elliptic curves in class 176610.cy have rank \(0\).

Modular form 176610.2.a.cy

sage: E.q_eigenform(10)
 
\( q + q^{2} - q^{3} + q^{4} + q^{5} - q^{6} + q^{7} + q^{8} + q^{9} + q^{10} - q^{12} + 2q^{13} + q^{14} - q^{15} + q^{16} + 6q^{17} + q^{18} - 8q^{19} + O(q^{20}) \)

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.