Properties

Label 8820.g
Number of curves 4
Conductor 8820
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("8820.g1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 8820.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
8820.g1 8820j3 [0, 0, 0, -18228, -947023] [2] 12960  
8820.g2 8820j4 [0, 0, 0, -16023, -1184722] [2] 25920  
8820.g3 8820j1 [0, 0, 0, -588, 3773] [2] 4320 \(\Gamma_0(N)\)-optimal
8820.g4 8820j2 [0, 0, 0, 1617, 25382] [2] 8640  

Rank

sage: E.rank()
 

The elliptic curves in class 8820.g have rank \(0\).

Modular form 8820.2.a.g

sage: E.q_eigenform(10)
 
\( q - q^{5} - 2q^{13} - 6q^{17} + 4q^{19} + O(q^{20}) \)

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 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.