Properties

Label 23534.o
Number of curves 6
Conductor 23534
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("23534.o1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 23534.o

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
23534.o1 23534e6 [1, 1, 0, -4590005, -3786930259] [2] 414720  
23534.o2 23534e5 [1, 1, 0, -286645, -59359827] [2] 207360  
23534.o3 23534e4 [1, 1, 0, -59710, -4628148] [2] 138240  
23534.o4 23534e2 [1, 1, 0, -17685, 897299] [2] 46080  
23534.o5 23534e1 [1, 1, 0, -875, 19817] [2] 23040 \(\Gamma_0(N)\)-optimal
23534.o6 23534e3 [1, 1, 0, 7530, -418924] [2] 69120  

Rank

sage: E.rank()
 

The elliptic curves in class 23534.o have rank \(1\).

Modular form 23534.2.a.o

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

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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 3 & 9 & 18 & 6 \\ 2 & 1 & 6 & 18 & 9 & 3 \\ 3 & 6 & 1 & 3 & 6 & 2 \\ 9 & 18 & 3 & 1 & 2 & 6 \\ 18 & 9 & 6 & 2 & 1 & 3 \\ 6 & 3 & 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.