Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("11088.n1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 11088.n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
11088.n1 11088bz3 [0, 0, 0, -13248651, 18561179194] [2] 368640  
11088.n2 11088bz2 [0, 0, 0, -830091, 288510010] [2, 2] 184320  
11088.n3 11088bz4 [0, 0, 0, -208011, 710902330] [4] 368640  
11088.n4 11088bz1 [0, 0, 0, -92811, -3600326] [2] 92160 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Modular form 11088.2.a.n

sage: E.q_eigenform(10)
 
\( q - 2q^{5} + q^{7} + q^{11} + 2q^{13} - 6q^{17} + 8q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.