Properties

Label 195195.bl
Number of curves $6$
Conductor $195195$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("195195.bl1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 195195.bl

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
195195.bl1 195195ca6 [1, 1, 0, -2239253, -1290613722] [2] 4718592  
195195.bl2 195195ca4 [1, 1, 0, -147878, -17802897] [2, 2] 2359296  
195195.bl3 195195ca2 [1, 1, 0, -45633, 3484512] [2, 2] 1179648  
195195.bl4 195195ca1 [1, 1, 0, -44788, 3629683] [2] 589824 \(\Gamma_0(N)\)-optimal
195195.bl5 195195ca3 [1, 1, 0, 43092, 15497877] [2] 2359296  
195195.bl6 195195ca5 [1, 1, 0, 307577, -105341348] [2] 4718592  

Rank

sage: E.rank()
 

The elliptic curves in class 195195.bl have rank \(0\).

Modular form 195195.2.a.bl

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.