Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("s1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 17325s

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
17325.n6 17325s1 [1, -1, 1, 7870, 78064872] [2] 184320 \(\Gamma_0(N)\)-optimal
17325.n5 17325s2 [1, -1, 1, -2693255, 1671728622] [2, 2] 368640  
17325.n4 17325s3 [1, -1, 1, -5725130, -2779063878] [2] 737280  
17325.n2 17325s4 [1, -1, 1, -42879380, 108084587622] [2, 2] 737280  
17325.n1 17325s5 [1, -1, 1, -686070005, 6916900543872] [2] 1474560  
17325.n3 17325s6 [1, -1, 1, -42666755, 109209373872] [2] 1474560  

Rank

sage: E.rank()
 

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

Complex multiplication

The elliptic curves in class 17325s do not have complex multiplication.

Modular form 17325.2.a.s

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

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.