Properties

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

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("11088.c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 11088bi

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
11088.c2 11088bi1 [0, 0, 0, 51, 191] [] 2304 \(\Gamma_0(N)\)-optimal
11088.c1 11088bi2 [0, 0, 0, -489, -7369] [] 6912  

Rank

sage: E.rank()
 

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

Modular form 11088.2.a.c

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

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.