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Properties

Label 17325k
Number of curves $2$
Conductor $17325$
CM no
Rank $0$
Graph

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

Elliptic curves in class 17325k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
17325.d2 17325k1 \([0, 0, 1, -2011575, -1285997594]\) \(-79028701534867456/16987307596875\) \(-193496050595654296875\) \([]\) \(1152000\) \(2.6138\) \(\Gamma_0(N)\)-optimal
17325.d1 17325k2 \([0, 0, 1, -6027825, 107691166156]\) \(-2126464142970105856/438611057788643355\) \(-4996054080123765715546875\) \([]\) \(5760000\) \(3.4185\)  

Rank

sage: E.rank()
 

The elliptic curves in class 17325k have rank \(0\).

Complex multiplication

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

Modular form 17325.2.a.k

sage: E.q_eigenform(10)
 
\(q - 2 q^{2} + 2 q^{4} - q^{7} - q^{11} + 6 q^{13} + 2 q^{14} - 4 q^{16} - 7 q^{17} - 5 q^{19} + O(q^{20})\) Copy content Toggle raw display

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.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.