Properties

Base field \(\Q(\sqrt{-3}) \)
Label 2.0.3.1-19200.1-g
Conductor 19200.1
Rank \( 1 \)

Related objects

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Base field \(\Q(\sqrt{-3}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x + 1 \); class number \(1\).

Elliptic curves in class 19200.1-g over \(\Q(\sqrt{-3}) \)

Isogeny class 19200.1-g contains 8 curves linked by isogenies of degrees dividing 16.

Curve label Weierstrass Coefficients
19200.1-g1 \( \bigl[0\) , \( 1\) , \( 0\) , \( -1760\) , \( 52788\bigr] \)
19200.1-g2 \( \bigl[0\) , \( 1\) , \( 0\) , \( 0\) , \( -12\bigr] \)
19200.1-g3 \( \bigl[0\) , \( 1\) , \( 0\) , \( 560\) , \( 2900\bigr] \)
19200.1-g4 \( \bigl[0\) , \( 1\) , \( 0\) , \( -160\) , \( 308\bigr] \)
19200.1-g5 \( \bigl[0\) , \( 1\) , \( 0\) , \( -80\) , \( -300\bigr] \)
19200.1-g6 \( \bigl[0\) , \( 1\) , \( 0\) , \( -2160\) , \( 37908\bigr] \)
19200.1-g7 \( \bigl[0\) , \( 1\) , \( 0\) , \( -1280\) , \( -18060\bigr] \)
19200.1-g8 \( \bigl[0\) , \( 1\) , \( 0\) , \( -34560\) , \( 2461428\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 16 & 8 & 4 & 8 & 2 & 16 & 4 \\ 16 & 1 & 8 & 4 & 2 & 8 & 4 & 16 \\ 8 & 8 & 1 & 2 & 4 & 4 & 8 & 8 \\ 4 & 4 & 2 & 1 & 2 & 2 & 4 & 4 \\ 8 & 2 & 4 & 2 & 1 & 4 & 2 & 8 \\ 2 & 8 & 4 & 2 & 4 & 1 & 8 & 2 \\ 16 & 4 & 8 & 4 & 2 & 8 & 1 & 16 \\ 4 & 16 & 8 & 4 & 8 & 2 & 16 & 1 \end{array}\right)\)

Isogeny graph