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Properties

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

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

Elliptic curves in class 476850.br

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
476850.br1 476850br6 \([1, 1, 0, -2110711650, -37320720081750]\) \(2757381641970898311361/379829992662450\) \(143252697752490321625781250\) \([2]\) \(339738624\) \(4.0365\)  
476850.br2 476850br4 \([1, 1, 0, -143705400, -472792000500]\) \(870220733067747361/247623269602500\) \(93390996188061661289062500\) \([2, 2]\) \(169869312\) \(3.6899\)  
476850.br3 476850br2 \([1, 1, 0, -53392900, 144313312000]\) \(44633474953947361/1967006250000\) \(741855454418847656250000\) \([2, 2]\) \(84934656\) \(3.3433\)  
476850.br4 476850br1 \([1, 1, 0, -52814900, 147712530000]\) \(43199583152847841/89760000\) \(33852940522500000000\) \([2]\) \(42467328\) \(2.9968\) \(\Gamma_0(N)\)-optimal*
476850.br5 476850br3 \([1, 1, 0, 27671600, 543880232500]\) \(6213165856218719/342407226562500\) \(-129138719644546508789062500\) \([2]\) \(169869312\) \(3.6899\)  
476850.br6 476850br5 \([1, 1, 0, 378300850, -3117797669250]\) \(15875306080318016639/20322604533582450\) \(-7664660456079050063500781250\) \([2]\) \(339738624\) \(4.0365\)  
*optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 0 curves highlighted, and conditionally curve 476850.br1.

Rank

sage: E.rank()
 

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

Complex multiplication

The elliptic curves in class 476850.br do not have complex multiplication.

Modular form 476850.2.a.br

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

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.