Properties

Label 11088br
Number of curves 4
Conductor 11088
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("11088.k1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 11088br

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
11088.k4 11088br1 [0, 0, 0, -531, -154926] [2] 18432 \(\Gamma_0(N)\)-optimal
11088.k3 11088br2 [0, 0, 0, -46611, -3832110] [2, 2] 36864  
11088.k1 11088br3 [0, 0, 0, -743571, -246792366] [2] 73728  
11088.k2 11088br4 [0, 0, 0, -86931, 3788370] [2] 73728  

Rank

sage: E.rank()
 

The elliptic curves in class 11088br have rank \(0\).

Modular form 11088.2.a.k

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

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.