Properties

Base field \(\Q(\sqrt{-1}) \)
Label 2.0.4.1-57800.6-d
Conductor 57800.6
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 57800.6-d over \(\Q(\sqrt{-1}) \)

Isogeny class 57800.6-d contains 10 curves linked by isogenies of degrees dividing 16.

Curve label Weierstrass Coefficients
57800.6-d1 \( \bigl[i + 1\) , \( i\) , \( 0\) , \( 104 i + 888\) , \( 10640 i - 1820\bigr] \)
57800.6-d2 \( \bigl[i + 1\) , \( i\) , \( 0\) , \( -796 i + 408\) , \( 936 i - 9924\bigr] \)
57800.6-d3 \( \bigl[i + 1\) , \( i\) , \( 0\) , \( -26 i + 48\) , \( 224 i - 208\bigr] \)
57800.6-d4 \( \bigl[i + 1\) , \( i\) , \( 0\) , \( -1166 i + 18\) , \( -12356 i - 7688\bigr] \)
57800.6-d5 \( \bigl[i + 1\) , \( i\) , \( 0\) , \( 634 i + 978\) , \( 9964 i + 11152\bigr] \)
57800.6-d6 \( \bigl[i + 1\) , \( i\) , \( 0\) , \( 14 i - 27\) , \( 22 i - 46\bigr] \)
57800.6-d7 \( \bigl[0\) , \( 0\) , \( 0\) , \( -16 i + 30\) , \( -52 i - 47\bigr] \)
57800.6-d8 \( \bigl[i + 1\) , \( i\) , \( 0\) , \( 214 i - 402\) , \( 2302 i - 2876\bigr] \)
57800.6-d9 \( \bigl[i + 1\) , \( i\) , \( 0\) , \( -12746 i + 6558\) , \( 51156 i - 652464\bigr] \)
57800.6-d10 \( \bigl[i + 1\) , \( i\) , \( 0\) , \( 1654 i + 14238\) , \( 657780 i - 114840\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph