Properties

Label 28322h
Number of curves 6
Conductor 28322
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("28322.c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 28322h

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
28322.c5 28322h1 [1, 0, 1, -7376, -494070] [2] 73728 \(\Gamma_0(N)\)-optimal
28322.c4 28322h2 [1, 0, 1, -148986, -22132078] [2] 147456  
28322.c6 28322h3 [1, 0, 1, 63429, 10324934] [2] 221184  
28322.c3 28322h4 [1, 0, 1, -503011, 112510710] [2] 442368  
28322.c2 28322h5 [1, 0, 1, -2414746, 1448261196] [2] 663552  
28322.c1 28322h6 [1, 0, 1, -38666906, 92542688844] [2] 1327104  

Rank

sage: E.rank()
 

The elliptic curves in class 28322h have rank \(0\).

Modular form 28322.2.a.c

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

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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.