Properties

Label 7220.f
Number of curves 4
Conductor 7220
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("7220.f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 7220.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
7220.f1 7220c3 [0, -1, 0, -14921, 706370] [2] 10368  
7220.f2 7220c4 [0, -1, 0, -13116, 881816] [2] 20736  
7220.f3 7220c1 [0, -1, 0, -481, -2634] [2] 3456 \(\Gamma_0(N)\)-optimal
7220.f4 7220c2 [0, -1, 0, 1324, -19240] [2] 6912  

Rank

sage: E.rank()
 

The elliptic curves in class 7220.f have rank \(1\).

Modular form 7220.2.a.f

sage: E.q_eigenform(10)
 
\( q + 2q^{3} - q^{5} + 2q^{7} + q^{9} - 2q^{13} - 2q^{15} - 6q^{17} + O(q^{20}) \)

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.