Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("17325.k1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 17325u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
17325.k4 17325u1 [1, -1, 1, -7655, -255778] [2] 20480 \(\Gamma_0(N)\)-optimal
17325.k3 17325u2 [1, -1, 1, -8780, -174778] [2, 2] 40960  
17325.k2 17325u3 [1, -1, 1, -63905, 6109472] [2, 2] 81920  
17325.k6 17325u4 [1, -1, 1, 28345, -1288528] [2] 81920  
17325.k1 17325u5 [1, -1, 1, -1016780, 394882472] [2] 163840  
17325.k5 17325u6 [1, -1, 1, 6970, 18866972] [2] 163840  

Rank

sage: E.rank()
 

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

Modular form 17325.2.a.k

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

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.