Properties

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

Related objects

Downloads

Learn more about

Show commands for: SageMath

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

Elliptic curves in class 24843d

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
24843.p6 24843d1 [1, 1, 0, 8109, 65304] 2 55296 \(\Gamma_0(N)\)-optimal
24843.p5 24843d2 [1, 1, 0, -33296, 487635] 4 110592  
24843.p3 24843d3 [1, 1, 0, -323131, -70406006] 2 221184  
24843.p2 24843d4 [1, 1, 0, -405941, 99238560] 4 221184  
24843.p4 24843d5 [1, 1, 0, -281726, 161271531] 2 442368  
24843.p1 24843d6 [1, 1, 0, -6492476, 6364717689] 2 442368  

Rank

sage: E.rank()

The elliptic curves in class 24843d 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 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.