Properties

Label 11088.bl
Number of curves 6
Conductor 11088
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("11088.bl1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 11088.bl

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
11088.bl1 11088bh5 [0, 0, 0, -650739, -202049678] [2] 81920  
11088.bl2 11088bh3 [0, 0, 0, -40899, -3119870] [2, 2] 40960  
11088.bl3 11088bh2 [0, 0, 0, -5619, 90610] [2, 2] 20480  
11088.bl4 11088bh1 [0, 0, 0, -4899, 131938] [2] 10240 \(\Gamma_0(N)\)-optimal
11088.bl5 11088bh6 [0, 0, 0, 4461, -9660782] [2] 81920  
11088.bl6 11088bh4 [0, 0, 0, 18141, 656098] [2] 40960  

Rank

sage: E.rank()
 

The elliptic curves in class 11088.bl have rank \(1\).

Modular form 11088.2.a.bl

sage: E.q_eigenform(10)
 
\( q + 2q^{5} - q^{7} - q^{11} + 6q^{13} - 2q^{17} - 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.