Properties

Label 3150.bo
Number of curves 6
Conductor 3150
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("3150.bo1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 3150.bo

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
3150.bo1 3150bl3 [1, -1, 1, -302405, -63931903] [2] 16384  
3150.bo2 3150bl5 [1, -1, 1, -205655, 35603597] [2] 32768  
3150.bo3 3150bl4 [1, -1, 1, -23405, -481903] [2, 2] 16384  
3150.bo4 3150bl2 [1, -1, 1, -18905, -994903] [2, 2] 8192  
3150.bo5 3150bl1 [1, -1, 1, -905, -22903] [2] 4096 \(\Gamma_0(N)\)-optimal
3150.bo6 3150bl6 [1, -1, 1, 86845, -3789403] [2] 32768  

Rank

sage: E.rank()
 

The elliptic curves in class 3150.bo have rank \(0\).

Modular form 3150.2.a.bo

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.