Properties

Label 146523.y
Number of curves $6$
Conductor $146523$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("146523.y1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 146523.y

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
146523.y1 146523s6 [1, 0, 1, -985319352, -11902817825819] [2] 49545216  
146523.y2 146523s4 [1, 0, 1, -67841167, -145885371955] [2, 2] 24772608  
146523.y3 146523s2 [1, 0, 1, -26570522, 50975604695] [2, 2] 12386304  
146523.y4 146523s1 [1, 0, 1, -26326317, 51989348491] [2] 6193152 \(\Gamma_0(N)\)-optimal
146523.y5 146523s3 [1, 0, 1, 10792843, 182957955221] [2] 24772608  
146523.y6 146523s5 [1, 0, 1, 189306698, -987890341111] [2] 49545216  

Rank

sage: E.rank()
 

The elliptic curves in class 146523.y have rank \(0\).

Modular form 146523.2.a.y

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{3} - q^{4} - 2q^{5} + q^{6} - 3q^{8} + q^{9} - 2q^{10} + 4q^{11} - q^{12} - 2q^{15} - q^{16} + q^{18} + 4q^{19} + O(q^{20}) \)

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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.