Properties

Label 24.a
Number of curves 6
Conductor 24
CM no
Rank 0
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("24.a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 24.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
24.a1 24a5 [0, -1, 0, -384, -2772] [2] 4  
24.a2 24a3 [0, -1, 0, -64, 220] [4] 2  
24.a3 24a2 [0, -1, 0, -24, -36] [2, 2] 2  
24.a4 24a1 [0, -1, 0, -4, 4] [2, 4] 1 \(\Gamma_0(N)\)-optimal
24.a5 24a4 [0, -1, 0, 1, 0] [4] 2  
24.a6 24a6 [0, -1, 0, 16, -180] [2] 4  

Rank

sage: E.rank()
 

The elliptic curves in class 24.a have rank \(0\).

Modular form 24.2.a.a

sage: E.q_eigenform(10)
 
\( q - q^{3} - 2q^{5} + q^{9} + 4q^{11} - 2q^{13} + 2q^{15} + 2q^{17} - 4q^{19} + O(q^{20}) \)

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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.