Properties

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

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("11088.m1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 11088.m

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
11088.m1 11088ca4 [0, 0, 0, -5795571, 5370224690] [2] 147456  
11088.m2 11088ca3 [0, 0, 0, -505011, 11749106] [2] 147456  
11088.m3 11088ca2 [0, 0, 0, -362451, 83798930] [2, 2] 73728  
11088.m4 11088ca1 [0, 0, 0, -13971, 2324306] [2] 36864 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Modular form 11088.2.a.m

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.