Properties

Label 176610.k
Number of curves $6$
Conductor $176610$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("k1")
 
E.isogeny_class()
 

Elliptic curves in class 176610.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
176610.k1 176610dj3 \([1, 1, 0, -291368672, 1914189162816]\) \(4599009330619965070321/426202560\) \(253515222157901760\) \([2]\) \(30965760\) \(3.2206\)  
176610.k2 176610dj6 \([1, 1, 0, -144260952, -651617326776]\) \(558190076008175760241/14707244541053400\) \(8748212040668504226341400\) \([2]\) \(61931520\) \(3.5672\)  
176610.k3 176610dj4 \([1, 1, 0, -20633952, 21432786624]\) \(1633364098002912241/611345405160000\) \(363642504175361736360000\) \([2, 2]\) \(30965760\) \(3.2206\)  
176610.k4 176610dj2 \([1, 1, 0, -18211872, 29898925056]\) \(1123051131566043121/341803929600\) \(203312948535522201600\) \([2, 2]\) \(15482880\) \(2.8741\)  
176610.k5 176610dj1 \([1, 1, 0, -988192, 594555904]\) \(-179415687049201/153259868160\) \(-91162543754953359360\) \([2]\) \(7741440\) \(2.5275\) \(\Gamma_0(N)\)-optimal
176610.k6 176610dj5 \([1, 1, 0, 64239768, 152698481976]\) \(49288727461474020239/45451852884375000\) \(-27035822078287366509375000\) \([2]\) \(61931520\) \(3.5672\)  

Rank

sage: E.rank()
 

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

Complex multiplication

The elliptic curves in class 176610.k do not have complex multiplication.

Modular form 176610.2.a.k

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{5} + q^{6} - q^{7} - q^{8} + q^{9} - q^{10} + 4 q^{11} - q^{12} - 2 q^{13} + q^{14} - q^{15} + q^{16} + 6 q^{17} - q^{18} + 4 q^{19} + O(q^{20})\) Copy content Toggle raw display

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.