Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("11088.i1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 11088p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
11088.i3 11088p1 [0, 0, 0, -5282751, -4673457794] [2] 184320 \(\Gamma_0(N)\)-optimal
11088.i2 11088p2 [0, 0, 0, -5282931, -4673123390] [2, 2] 368640  
11088.i1 11088p3 [0, 0, 0, -5762091, -3774890054] [2] 737280  
11088.i4 11088p4 [0, 0, 0, -4806651, -5549954870] [4] 737280  

Rank

sage: E.rank()
 

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

Modular form 11088.2.a.i

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

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 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.