Properties

Label 221760iq
Number of curves $6$
Conductor $221760$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("iq1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 221760iq

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
221760.lq6 221760iq1 [0, 0, 0, 20148, 319761776] [2] 3932160 \(\Gamma_0(N)\)-optimal
221760.lq5 221760iq2 [0, 0, 0, -6894732, 6844642544] [2, 2] 7864320  
221760.lq2 221760iq3 [0, 0, 0, -109771212, 442670562416] [2, 2] 15728640  
221760.lq4 221760iq4 [0, 0, 0, -14656332, -11388908176] [2] 15728640  
221760.lq1 221760iq5 [0, 0, 0, -1756339212, 28330922092016] [2] 31457280  
221760.lq3 221760iq6 [0, 0, 0, -109226892, 447277904624] [2] 31457280  

Rank

sage: E.rank()
 

The elliptic curves in class 221760iq have rank \(0\).

Complex multiplication

The elliptic curves in class 221760iq do not have complex multiplication.

Modular form 221760.2.a.iq

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

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.