Properties

Label 221760fa
Number of curves 4
Conductor 221760
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("221760.dd1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 221760fa

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
221760.dd3 221760fa1 [0, 0, 0, -32268, 43416592] [2] 2654208 \(\Gamma_0(N)\)-optimal
221760.dd2 221760fa2 [0, 0, 0, -2059788, 1127734288] [2] 5308416  
221760.dd4 221760fa3 [0, 0, 0, 290292, -1169538032] [2] 7962624  
221760.dd1 221760fa4 [0, 0, 0, -15042828, -21820184048] [2] 15925248  

Rank

sage: E.rank()
 

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

Modular form 221760.2.a.dd

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

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.