Properties

Label 221760be
Number of curves $6$
Conductor $221760$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("221760.mb1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 221760be

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
221760.mb4 221760be1 [0, 0, 0, -152652, 22956176] [2] 1048576 \(\Gamma_0(N)\)-optimal
221760.mb3 221760be2 [0, 0, 0, -155532, 22044944] [2, 2] 2097152  
221760.mb5 221760be3 [0, 0, 0, 146868, 97403024] [2] 4194304  
221760.mb2 221760be4 [0, 0, 0, -504012, -111631984] [2, 2] 4194304  
221760.mb6 221760be5 [0, 0, 0, 1048308, -663636976] [2] 8388608  
221760.mb1 221760be6 [0, 0, 0, -7632012, -8114950384] [2] 8388608  

Rank

sage: E.rank()
 

The elliptic curves in class 221760be have rank \(1\).

Modular form 221760.2.a.mb

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

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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.