Properties

Label 24843.p
Number of curves 6
Conductor 24843
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("24843.p1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 24843.p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
24843.p1 24843d6 [1, 1, 0, -6492476, 6364717689] [2] 442368  
24843.p2 24843d4 [1, 1, 0, -405941, 99238560] [2, 2] 221184  
24843.p3 24843d3 [1, 1, 0, -323131, -70406006] [2] 221184  
24843.p4 24843d5 [1, 1, 0, -281726, 161271531] [2] 442368  
24843.p5 24843d2 [1, 1, 0, -33296, 487635] [2, 2] 110592  
24843.p6 24843d1 [1, 1, 0, 8109, 65304] [2] 55296 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 24843.p have rank \(0\).

Modular form 24843.2.a.p

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

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.