Properties

Label 104742.bv
Number of curves 4
Conductor 104742
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("104742.bv1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 104742.bv

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
104742.bv1 104742bl3 [1, -1, 1, -383360, -90914461] [2] 1140480  
104742.bv2 104742bl4 [1, -1, 1, -192920, -181411549] [2] 2280960  
104742.bv3 104742bl1 [1, -1, 1, -26285, 1553681] [2] 380160 \(\Gamma_0(N)\)-optimal
104742.bv4 104742bl2 [1, -1, 1, 21325, 6524165] [2] 760320  

Rank

sage: E.rank()
 

The elliptic curves in class 104742.bv have rank \(0\).

Modular form 104742.2.a.bv

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{4} - 2q^{7} + q^{8} - q^{11} - 4q^{13} - 2q^{14} + q^{16} - 6q^{17} + 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.