Properties

Label 273600.pq
Number of curves $4$
Conductor $273600$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("273600.pq1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 273600.pq

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
273600.pq1 273600pq3 [0, 0, 0, -43776300, 111482498000] [2] 14155776  
273600.pq2 273600pq4 [0, 0, 0, -3168300, 1154882000] [2] 14155776  
273600.pq3 273600pq2 [0, 0, 0, -2736300, 1741538000] [2, 2] 7077888  
273600.pq4 273600pq1 [0, 0, 0, -144300, 36002000] [2] 3538944 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 273600.pq have rank \(1\).

Modular form 273600.2.a.pq

sage: E.q_eigenform(10)
 
\( q + 4q^{7} + 4q^{11} - 2q^{13} - 2q^{17} - q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.