Properties

Label 24255bm
Number of curves $6$
Conductor $24255$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("24255.bn1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 24255bm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
24255.bn4 24255bm1 [1, -1, 0, -116874, 15408063] [2] 98304 \(\Gamma_0(N)\)-optimal
24255.bn3 24255bm2 [1, -1, 0, -119079, 14798160] [2, 2] 196608  
24255.bn5 24255bm3 [1, -1, 0, 112446, 65224305] [2] 393216  
24255.bn2 24255bm4 [1, -1, 0, -385884, -74688237] [2, 2] 393216  
24255.bn6 24255bm5 [1, -1, 0, 802611, -444785580] [2] 786432  
24255.bn1 24255bm6 [1, -1, 0, -5843259, -5434921962] [2] 786432  

Rank

sage: E.rank()
 

The elliptic curves in class 24255bm have rank \(0\).

Modular form 24255.2.a.bn

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

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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.