Properties

Label 2310.h
Number of curves 8
Conductor 2310
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("2310.h1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 2310.h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
2310.h1 2310g7 [1, 0, 1, -25467989, -49471735264] [2] 165888  
2310.h2 2310g6 [1, 0, 1, -1616469, -747850208] [2, 2] 82944  
2310.h3 2310g4 [1, 0, 1, -437774, -9825928] [6] 55296  
2310.h4 2310g3 [1, 0, 1, -305749, 50640416] [2] 41472  
2310.h5 2310g2 [1, 0, 1, -286854, 58872856] [2, 6] 27648  
2310.h6 2310g1 [1, 0, 1, -286534, 59011352] [6] 13824 \(\Gamma_0(N)\)-optimal
2310.h7 2310g5 [1, 0, 1, -141054, 118709176] [6] 55296  
2310.h8 2310g8 [1, 0, 1, 1263531, -3122122208] [2] 165888  

Rank

sage: E.rank()
 

The elliptic curves in class 2310.h have rank \(1\).

Modular form 2310.2.a.h

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{3} + q^{4} - q^{5} - q^{6} + q^{7} - q^{8} + q^{9} + q^{10} - q^{11} + q^{12} + 2q^{13} - q^{14} - q^{15} + q^{16} - 6q^{17} - q^{18} - 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 3 & 4 & 6 & 12 & 12 & 4 \\ 2 & 1 & 6 & 2 & 3 & 6 & 6 & 2 \\ 3 & 6 & 1 & 12 & 2 & 4 & 4 & 12 \\ 4 & 2 & 12 & 1 & 6 & 3 & 12 & 4 \\ 6 & 3 & 2 & 6 & 1 & 2 & 2 & 6 \\ 12 & 6 & 4 & 3 & 2 & 1 & 4 & 12 \\ 12 & 6 & 4 & 12 & 2 & 4 & 1 & 3 \\ 4 & 2 & 12 & 4 & 6 & 12 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.