Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("221760.fl1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 221760de

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
221760.fl3 221760de1 [0, 0, 0, -288588, -51813232] [2] 2359296 \(\Gamma_0(N)\)-optimal
221760.fl2 221760de2 [0, 0, 0, -1221708, 468121232] [2, 2] 4718592  
221760.fl1 221760de3 [0, 0, 0, -19002828, 31883804048] [2] 9437184  
221760.fl4 221760de4 [0, 0, 0, 1629492, 2328244112] [2] 9437184  

Rank

sage: E.rank()
 

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

Modular form 221760.2.a.fl

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.