Properties

Label 11088cb
Number of curves 2
Conductor 11088
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("11088.l1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 11088cb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
11088.l2 11088cb1 [0, 0, 0, -2091, -38054] [2] 9216 \(\Gamma_0(N)\)-optimal
11088.l1 11088cb2 [0, 0, 0, -33771, -2388710] [2] 18432  

Rank

sage: E.rank()
 

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

Modular form 11088.2.a.l

sage: E.q_eigenform(10)
 
\( q - 2q^{5} + q^{7} + q^{11} - 4q^{13} - 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.