Properties

Label 11088.b
Number of curves 3
Conductor 11088
CM no
Rank 1
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("11088.b1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 11088.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
11088.b1 11088bj1 [0, 0, 0, -12864, 561584] [] 14400 \(\Gamma_0(N)\)-optimal
11088.b2 11088bj2 [0, 0, 0, -7104, 1065584] [] 43200  
11088.b3 11088bj3 [0, 0, 0, 63456, -27581776] [] 129600  

Rank

sage: E.rank()
 

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

Modular form 11088.2.a.b

sage: E.q_eigenform(10)
 
\( q - 3q^{5} - q^{7} - q^{11} - 4q^{13} + 6q^{17} - 2q^{19} + O(q^{20}) \)

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 LMFDB numbering.

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.