Properties

Label 17160.a
Number of curves $4$
Conductor $17160$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 17160.a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
17160.a1 17160b4 \([0, -1, 0, -25660856, 50041356300]\) \(912446049969377120252018/17177299425\) \(35179109222400\) \([2]\) \(688128\) \(2.5873\)  
17160.a2 17160b3 \([0, -1, 0, -1746856, 634609900]\) \(287849398425814280018/81784533026485575\) \(167494723638242457600\) \([2]\) \(688128\) \(2.5873\)  
17160.a3 17160b2 \([0, -1, 0, -1603856, 782243100]\) \(445574312599094932036/61129333175625\) \(62596437171840000\) \([2, 2]\) \(344064\) \(2.2408\)  
17160.a4 17160b1 \([0, -1, 0, -91356, 14498100]\) \(-329381898333928144/162600887109375\) \(-41625827100000000\) \([2]\) \(172032\) \(1.8942\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 17160.a have rank \(0\).

Complex multiplication

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

Modular form 17160.2.a.a

sage: E.q_eigenform(10)
 
\(q - q^{3} - q^{5} - 4 q^{7} + q^{9} - q^{11} + q^{13} + q^{15} - 2 q^{17} + 4 q^{19} + O(q^{20})\) 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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.