Properties

Label 126960ba
Number of curves $6$
Conductor $126960$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("126960.q1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 126960ba

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
126960.q5 126960ba1 [0, -1, 0, -3555056, 2831716800] [2] 4866048 \(\Gamma_0(N)\)-optimal
126960.q4 126960ba2 [0, -1, 0, -58401776, 171803491776] [2, 2] 9732096  
126960.q3 126960ba3 [0, -1, 0, -59925296, 162368637120] [2, 2] 19464192  
126960.q1 126960ba4 [0, -1, 0, -934425776, 10994554397376] [4] 19464192  
126960.q6 126960ba5 [0, -1, 0, 74398384, 786597642816] [2] 38928384  
126960.q2 126960ba6 [0, -1, 0, -218625296, -1065715442880] [2] 38928384  

Rank

sage: E.rank()
 

The elliptic curves in class 126960ba have rank \(1\).

Modular form 126960.2.a.q

sage: E.q_eigenform(10)
 
\( q - q^{3} - q^{5} + q^{9} + 4q^{11} - 2q^{13} + q^{15} + 6q^{17} + 4q^{19} + O(q^{20}) \)

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 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.