Properties

Label 28749.h
Number of curves 6
Conductor 28749
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("28749.h1")
sage: E.isogeny_class()

Elliptic curves in class 28749.h

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
28749.h1 28749e6 [1, 0, 1, -1073325, -428090351] 2 202752  
28749.h2 28749e4 [1, 0, 1, -67110, -6687509] 4 101376  
28749.h3 28749e3 [1, 0, 1, -53420, 4718999] 2 101376  
28749.h4 28749e5 [1, 0, 1, -46575, -10852007] 2 202752  
28749.h5 28749e2 [1, 0, 1, -5505, -34169] 4 50688  
28749.h6 28749e1 [1, 0, 1, 1340, -4051] 2 25344 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()

The elliptic curves in class 28749.h have rank \(0\).

Modular form 28749.2.a.h

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

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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 8 & 4 & 4 & 8 \\ 2 & 1 & 4 & 2 & 2 & 4 \\ 8 & 4 & 1 & 8 & 2 & 4 \\ 4 & 2 & 8 & 1 & 4 & 8 \\ 4 & 2 & 2 & 4 & 1 & 2 \\ 8 & 4 & 4 & 8 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.