Properties

Label 43350.bk
Number of curves 6
Conductor 43350
CM no
Rank 0
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("43350.bk1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 43350.bk

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
43350.bk1 43350ba6 [1, 0, 1, -200450551, -1092359612752] [2] 4718592  
43350.bk2 43350ba4 [1, 0, 1, -12528301, -17068498252] [2, 2] 2359296  
43350.bk3 43350ba5 [1, 0, 1, -11878051, -18919109752] [2] 4718592  
43350.bk4 43350ba2 [1, 0, 1, -823801, -237427252] [2, 2] 1179648  
43350.bk5 43350ba1 [1, 0, 1, -245801, 43480748] [2] 589824 \(\Gamma_0(N)\)-optimal
43350.bk6 43350ba3 [1, 0, 1, 1632699, -1382156252] [2] 2359296  

Rank

sage: E.rank()
 

The elliptic curves in class 43350.bk have rank \(0\).

Modular form 43350.2.a.bk

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{3} + q^{4} - q^{6} - q^{8} + q^{9} + 4q^{11} + q^{12} + 2q^{13} + q^{16} - q^{18} + 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.