Properties

Label 221760lg
Number of curves 4
Conductor 221760
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("221760.es1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 221760lg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
221760.es3 221760lg1 [0, 0, 0, -32268, -43416592] [2] 2654208 \(\Gamma_0(N)\)-optimal
221760.es2 221760lg2 [0, 0, 0, -2059788, -1127734288] [2] 5308416  
221760.es4 221760lg3 [0, 0, 0, 290292, 1169538032] [2] 7962624  
221760.es1 221760lg4 [0, 0, 0, -15042828, 21820184048] [2] 15925248  

Rank

sage: E.rank()
 

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

Modular form 221760.2.a.es

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.