Properties

Label 17160n
Number of curves $2$
Conductor $17160$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("n1")
 
E.isogeny_class()
 

Elliptic curves in class 17160n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
17160.e2 17160n1 \([0, -1, 0, 584, -75620]\) \(21474271004/2412470775\) \(-2470370073600\) \([2]\) \(27648\) \(1.0573\) \(\Gamma_0(N)\)-optimal
17160.e1 17160n2 \([0, -1, 0, -23616, -1343700]\) \(711264560340098/26281975005\) \(53825484810240\) \([2]\) \(55296\) \(1.4039\)  

Rank

sage: E.rank()
 

The elliptic curves in class 17160n have rank \(1\).

Complex multiplication

The elliptic curves in class 17160n do not have complex multiplication.

Modular form 17160.2.a.n

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} - 2 q^{7} + q^{9} + q^{11} - q^{13} + q^{15} + 2 q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.