Properties

Label 17424.by
Number of curves 4
Conductor 17424
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("17424.by1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 17424.by

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
17424.by1 17424bw3 [0, 0, 0, -2552979, -1568527598] [2] 368640  
17424.by2 17424bw2 [0, 0, 0, -200739, -10874270] [2, 2] 184320  
17424.by3 17424bw1 [0, 0, 0, -113619, 14617042] [2] 92160 \(\Gamma_0(N)\)-optimal
17424.by4 17424bw4 [0, 0, 0, 757581, -84664910] [2] 368640  

Rank

sage: E.rank()
 

The elliptic curves in class 17424.by have rank \(0\).

Modular form 17424.2.a.by

sage: E.q_eigenform(10)
 
\( q + 2q^{5} + 4q^{7} + 2q^{13} - 2q^{17} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.