Properties

Label 220.a
Number of curves 4
Conductor 220
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("220.a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 220.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
220.a1 220a4 [0, 1, 0, -7100, -232652] [2] 216  
220.a2 220a3 [0, 1, 0, -445, -3720] [2] 108  
220.a3 220a2 [0, 1, 0, -100, -252] [6] 72  
220.a4 220a1 [0, 1, 0, -45, 100] [6] 36 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 220.a have rank \(1\).

Modular form 220.2.a.a

sage: E.q_eigenform(10)
 
\( q - 2q^{3} + q^{5} - 4q^{7} + q^{9} - q^{11} - 4q^{13} - 2q^{15} - 4q^{19} + O(q^{20}) \)

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 LMFDB 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 LMFDB labels.