Properties

Label 17136.bg
Number of curves $6$
Conductor $17136$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("17136.bg1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 17136.bg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
17136.bg1 17136y5 [0, 0, 0, -1975478979, -33795331366718] [2] 5898240  
17136.bg2 17136y3 [0, 0, 0, -123702339, -525941897150] [2, 2] 2949120  
17136.bg3 17136y6 [0, 0, 0, -42134979, -1209166417982] [2] 5898240  
17136.bg4 17136y2 [0, 0, 0, -13064259, 4567696450] [2, 2] 1474560  
17136.bg5 17136y1 [0, 0, 0, -10115139, 12366939202] [2] 737280 \(\Gamma_0(N)\)-optimal
17136.bg6 17136y4 [0, 0, 0, 50387901, 35925753922] [2] 2949120  

Rank

sage: E.rank()
 

The elliptic curves in class 17136.bg have rank \(1\).

Modular form 17136.2.a.bg

sage: E.q_eigenform(10)
 
\( q + 2q^{5} - q^{7} + 4q^{11} - 2q^{13} - q^{17} - 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.