Properties

Label 2800.g
Number of curves 6
Conductor 2800
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("2800.g1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 2800.g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
2800.g1 2800v6 [0, 1, 0, -1092208, 438981588] [2] 20736  
2800.g2 2800v5 [0, 1, 0, -68208, 6853588] [2] 10368  
2800.g3 2800v4 [0, 1, 0, -14208, 529588] [2] 6912  
2800.g4 2800v2 [0, 1, 0, -4208, -106412] [2] 2304  
2800.g5 2800v1 [0, 1, 0, -208, -2412] [2] 1152 \(\Gamma_0(N)\)-optimal
2800.g6 2800v3 [0, 1, 0, 1792, 49588] [2] 3456  

Rank

sage: E.rank()
 

The elliptic curves in class 2800.g have rank \(1\).

Modular form 2800.2.a.g

sage: E.q_eigenform(10)
 
\( q - 2q^{3} + q^{7} + q^{9} + 4q^{13} - 6q^{17} - 2q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 3 & 9 & 18 & 6 \\ 2 & 1 & 6 & 18 & 9 & 3 \\ 3 & 6 & 1 & 3 & 6 & 2 \\ 9 & 18 & 3 & 1 & 2 & 6 \\ 18 & 9 & 6 & 2 & 1 & 3 \\ 6 & 3 & 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.