Properties

Label 111090br
Number of curves $6$
Conductor $111090$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("111090.bn1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 111090br

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
111090.bn6 111090br1 [1, 1, 1, 5279, 208799] [2] 360448 \(\Gamma_0(N)\)-optimal
111090.bn5 111090br2 [1, 1, 1, -37041, 2121663] [2, 2] 720896  
111090.bn4 111090br3 [1, 1, 1, -195741, -31586217] [2] 1441792  
111090.bn2 111090br4 [1, 1, 1, -555461, 159099239] [2, 2] 1441792  
111090.bn3 111090br5 [1, 1, 1, -518431, 181272803] [2] 2883584  
111090.bn1 111090br6 [1, 1, 1, -8887211, 10193858939] [2] 2883584  

Rank

sage: E.rank()
 

The elliptic curves in class 111090br have rank \(1\).

Modular form 111090.2.a.bn

sage: E.q_eigenform(10)
 
\( q + q^{2} - q^{3} + q^{4} - q^{5} - q^{6} - q^{7} + q^{8} + q^{9} - q^{10} - 4q^{11} - q^{12} - 2q^{13} - q^{14} + q^{15} + q^{16} - 2q^{17} + q^{18} + 4q^{19} + O(q^{20}) \)

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 Cremona 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 Cremona labels.