Properties

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

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("17424.bi1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 17424.bi

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
17424.bi1 17424bm3 [0, 0, 0, -1402995, 637184306] [2] 276480  
17424.bi2 17424bm4 [0, 0, 0, -706035, 1270442162] [2] 552960  
17424.bi3 17424bm1 [0, 0, 0, -96195, -10831678] [2] 92160 \(\Gamma_0(N)\)-optimal
17424.bi4 17424bm2 [0, 0, 0, 78045, -45714526] [2] 184320  

Rank

sage: E.rank()
 

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

Modular form 17424.2.a.bi

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

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.