Properties

Label 28224.dh
Number of curves 6
Conductor 28224
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("28224.dh1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 28224.dh

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
28224.dh1 28224bi6 [0, 0, 0, -77066220, -260401928528] [2] 1327104  
28224.dh2 28224bi5 [0, 0, 0, -4812780, -4075624784] [2] 663552  
28224.dh3 28224bi4 [0, 0, 0, -1002540, -316696016] [2] 442368  
28224.dh4 28224bi2 [0, 0, 0, -296940, 62239408] [2] 147456  
28224.dh5 28224bi1 [0, 0, 0, -14700, 1388464] [2] 73728 \(\Gamma_0(N)\)-optimal
28224.dh6 28224bi3 [0, 0, 0, 126420, -29037008] [2] 221184  

Rank

sage: E.rank()
 

The elliptic curves in class 28224.dh have rank \(1\).

Modular form 28224.2.a.dh

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

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.