Properties

Label 130050br
Number of curves 6
Conductor 130050
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("130050.fm1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 130050br

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
130050.fm5 130050br1 [1, -1, 1, -2212205, -1173980203] [2] 4718592 \(\Gamma_0(N)\)-optimal
130050.fm4 130050br2 [1, -1, 1, -7414205, 6410535797] [2, 2] 9437184  
130050.fm2 130050br3 [1, -1, 1, -112754705, 460849452797] [2, 2] 18874368  
130050.fm6 130050br4 [1, -1, 1, 14694295, 37318218797] [2] 18874368  
130050.fm1 130050br5 [1, -1, 1, -1804054955, 29493709544297] [2] 37748736  
130050.fm3 130050br6 [1, -1, 1, -106902455, 510815963297] [2] 37748736  

Rank

sage: E.rank()
 

The elliptic curves in class 130050br have rank \(1\).

Modular form 130050.2.a.fm

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

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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.