Properties

Label 24150bc
Number of curves $6$
Conductor $24150$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("24150.y1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 24150bc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
24150.y5 24150bc1 [1, 0, 1, 3149, 139598] [2] 65536 \(\Gamma_0(N)\)-optimal
24150.y4 24150bc2 [1, 0, 1, -28851, 1611598] [2, 2] 131072  
24150.y3 24150bc3 [1, 0, 1, -126851, -15832402] [2, 2] 262144  
24150.y2 24150bc4 [1, 0, 1, -442851, 113391598] [2] 262144  
24150.y6 24150bc5 [1, 0, 1, 156649, -76501402] [2] 524288  
24150.y1 24150bc6 [1, 0, 1, -1978351, -1071187402] [2] 524288  

Rank

sage: E.rank()
 

The elliptic curves in class 24150bc have rank \(1\).

Modular form 24150.2.a.y

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

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.