Properties

Label 176001.d
Number of curves $6$
Conductor $176001$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("176001.d1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 176001.d

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
176001.d1 176001d3 [1, 0, 0, -59136342, 175032046917] [2] 7864320  
176001.d2 176001d6 [1, 0, 0, -12273547, -13455000118] [2] 15728640  
176001.d3 176001d4 [1, 0, 0, -3766832, 2624392575] [2, 2] 7864320  
176001.d4 176001d2 [1, 0, 0, -3696027, 2734635960] [2, 2] 3932160  
176001.d5 176001d1 [1, 0, 0, -226582, 44428307] [2] 1966080 \(\Gamma_0(N)\)-optimal
176001.d6 176001d5 [1, 0, 0, 3607003, 11648491848] [2] 15728640  

Rank

sage: E.rank()
 

The elliptic curves in class 176001.d have rank \(0\).

Modular form 176001.2.a.d

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.