Properties

Label 17600.w
Number of curves 4
Conductor 17600
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("17600.w1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 17600.w

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
17600.w1 17600r4 [0, 1, 0, -710033, -230521937] [2] 165888  
17600.w2 17600r3 [0, 1, 0, -44533, -3586437] [2] 82944  
17600.w3 17600r2 [0, 1, 0, -10033, -221937] [2] 55296  
17600.w4 17600r1 [0, 1, 0, -4533, 113563] [2] 27648 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 17600.w have rank \(0\).

Modular form 17600.2.a.w

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

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 LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.