Properties

Label 11088bf
Number of curves 4
Conductor 11088
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("11088.u1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 11088bf

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
11088.u4 11088bf1 [0, 0, 0, 11085, 267122] [2] 18432 \(\Gamma_0(N)\)-optimal
11088.u3 11088bf2 [0, 0, 0, -52275, 2307314] [2] 36864  
11088.u2 11088bf3 [0, 0, 0, -118515, -19945294] [2] 55296  
11088.u1 11088bf4 [0, 0, 0, -2035155, -1117413358] [2] 110592  

Rank

sage: E.rank()
 

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

Modular form 11088.2.a.u

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

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.