Properties

Label 17424by
Number of curves 2
Conductor 17424
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("17424.l1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 17424by

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
17424.l2 17424by1 [0, 0, 0, 2904, 33275] [2] 23040 \(\Gamma_0(N)\)-optimal
17424.l1 17424by2 [0, 0, 0, -13431, 284834] [2] 46080  

Rank

sage: E.rank()
 

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

Modular form 17424.2.a.l

sage: E.q_eigenform(10)
 
\( q - 2q^{5} - 2q^{7} + 2q^{13} + 4q^{17} - 6q^{19} + O(q^{20}) \)

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 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.