Properties

Label 17325y
Number of curves $6$
Conductor $17325$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("17325.p1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 17325y

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
17325.p4 17325y1 [1, -1, 1, -59630, -5589628] [2] 49152 \(\Gamma_0(N)\)-optimal
17325.p3 17325y2 [1, -1, 1, -60755, -5366878] [2, 2] 98304  
17325.p2 17325y3 [1, -1, 1, -196880, 27303122] [2, 2] 196608  
17325.p5 17325y4 [1, -1, 1, 57370, -23794378] [2] 196608  
17325.p1 17325y5 [1, -1, 1, -2981255, 1981934372] [2] 393216  
17325.p6 17325y6 [1, -1, 1, 409495, 161918372] [2] 393216  

Rank

sage: E.rank()
 

The elliptic curves in class 17325y have rank \(1\).

Modular form 17325.2.a.p

sage: E.q_eigenform(10)
 
\( q - q^{2} - q^{4} + q^{7} + 3q^{8} - q^{11} + 2q^{13} - q^{14} - q^{16} - 6q^{17} - 4q^{19} + O(q^{20}) \)

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.