Properties

Label 25230p
Number of curves 8
Conductor 25230
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("25230.o1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 25230p

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
25230.o8 25230p1 [1, 1, 1, 1244, 52373] [2] 48384 \(\Gamma_0(N)\)-optimal
25230.o6 25230p2 [1, 1, 1, -15576, 671349] [2, 2] 96768  
25230.o7 25230p3 [1, 1, 1, -11371, -1532071] [2] 145152  
25230.o5 25230p4 [1, 1, 1, -57626, -4610131] [2] 193536  
25230.o4 25230p5 [1, 1, 1, -242646, 45903693] [2] 193536  
25230.o3 25230p6 [1, 1, 1, -280491, -57186087] [2, 2] 290304  
25230.o1 25230p7 [1, 1, 1, -4485491, -3658348087] [2] 580608  
25230.o2 25230p8 [1, 1, 1, -381411, -12498711] [2] 580608  

Rank

sage: E.rank()
 

The elliptic curves in class 25230p have rank \(0\).

Modular form 25230.2.a.o

sage: E.q_eigenform(10)
 
\( q + q^{2} - q^{3} + q^{4} - q^{5} - q^{6} - 4q^{7} + q^{8} + q^{9} - q^{10} - q^{12} + 2q^{13} - 4q^{14} + q^{15} + q^{16} - 6q^{17} + q^{18} + 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 3 & 4 & 4 & 6 & 12 & 12 \\ 2 & 1 & 6 & 2 & 2 & 3 & 6 & 6 \\ 3 & 6 & 1 & 12 & 12 & 2 & 4 & 4 \\ 4 & 2 & 12 & 1 & 4 & 6 & 3 & 12 \\ 4 & 2 & 12 & 4 & 1 & 6 & 12 & 3 \\ 6 & 3 & 2 & 6 & 6 & 1 & 2 & 2 \\ 12 & 6 & 4 & 3 & 12 & 2 & 1 & 4 \\ 12 & 6 & 4 & 12 & 3 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.