Properties

Base field \(\Q(\sqrt{-1}) \)
Label 2.0.4.1-57600.2-g
Conductor 57600.2
Rank \( 0 \)

Related objects

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Base field \(\Q(\sqrt{-1}) \)

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

Elliptic curves in class 57600.2-g over \(\Q(\sqrt{-1}) \)

Isogeny class 57600.2-g contains 10 curves linked by isogenies of degrees dividing 16.

Curve label Weierstrass Coefficients
57600.2-g1 \( \bigl[0\) , \( i\) , \( 0\) , \( 1680 i - 6320\) , \( -80084 i + 187488\bigr] \)
57600.2-g2 \( \bigl[0\) , \( i\) , \( 0\) , \( -1680 i - 6320\) , \( -80084 i - 187488\bigr] \)
57600.2-g3 \( \bigl[0\) , \( i\) , \( 0\) , \( 1760\) , \( -52788 i\bigr] \)
57600.2-g4 \( \bigl[0\) , \( i\) , \( 0\) , \( 0\) , \( 12 i\bigr] \)
57600.2-g5 \( \bigl[0\) , \( i\) , \( 0\) , \( -560\) , \( -2900 i\bigr] \)
57600.2-g6 \( \bigl[0\) , \( i\) , \( 0\) , \( 160\) , \( -308 i\bigr] \)
57600.2-g7 \( \bigl[0\) , \( i\) , \( 0\) , \( 80\) , \( 300 i\bigr] \)
57600.2-g8 \( \bigl[0\) , \( i\) , \( 0\) , \( 2160\) , \( -37908 i\bigr] \)
57600.2-g9 \( \bigl[0\) , \( i\) , \( 0\) , \( 1280\) , \( 18060 i\bigr] \)
57600.2-g10 \( \bigl[0\) , \( i\) , \( 0\) , \( 34560\) , \( -2461428 i\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph