Properties

Label 11088.o
Number of curves 4
Conductor 11088
CM no
Rank 0
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("11088.o1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 11088.o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
11088.o1 11088y3 [0, 0, 0, -342291, -77079886] [2] 65536  
11088.o2 11088y4 [0, 0, 0, -49251, 2498690] [2] 65536  
11088.o3 11088y2 [0, 0, 0, -21531, -1188070] [2, 2] 32768  
11088.o4 11088y1 [0, 0, 0, 249, -59866] [2] 16384 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 11088.o have rank \(0\).

Modular form 11088.2.a.o

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

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.