Properties

Label 476850.br
Number of curves 6
Conductor 476850
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("476850.br1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 476850.br

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
476850.br1 476850br6 [1, 1, 0, -2110711650, -37320720081750] [u'2'] 339738624  
476850.br2 476850br4 [1, 1, 0, -143705400, -472792000500] [u'2', u'2'] 169869312  
476850.br3 476850br2 [1, 1, 0, -53392900, 144313312000] [u'2', u'2'] 84934656  
476850.br4 476850br1 [1, 1, 0, -52814900, 147712530000] [u'2'] 42467328 \(\Gamma_0(N)\)-optimal
476850.br5 476850br3 [1, 1, 0, 27671600, 543880232500] [u'2'] 169869312  
476850.br6 476850br5 [1, 1, 0, 378300850, -3117797669250] [u'2'] 339738624  

Rank

sage: E.rank()
 

The elliptic curves in class 476850.br have rank \(0\).

Modular form 476850.2.a.br

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.