Properties

Base field \(\Q(\sqrt{-1}) \)
Label 2.0.4.1-32000.2-l
Conductor 32000.2
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 32000.2-l over \(\Q(\sqrt{-1}) \)

Isogeny class 32000.2-l contains 10 curves linked by isogenies of degrees dividing 16.

Curve label Weierstrass Coefficients
32000.2-l1 \( \bigl[0\) , \( 0\) , \( 0\) , \( 1052 i + 39\) , \( 8774 i + 9868\bigr] \)
32000.2-l2 \( \bigl[0\) , \( 0\) , \( 0\) , \( 332 i + 999\) , \( 11686 i - 6148\bigr] \)
32000.2-l3 \( \bigl[0\) , \( 0\) , \( 0\) , \( 52 i + 39\) , \( 374 i + 68\bigr] \)
32000.2-l4 \( \bigl[0\) , \( 0\) , \( 0\) , \( -188 i + 1359\) , \( 654 i - 18972\bigr] \)
32000.2-l5 \( \bigl[0\) , \( 0\) , \( 0\) , \( 1252 i - 561\) , \( -6066 i + 17988\bigr] \)
32000.2-l6 \( \bigl[0\) , \( 0\) , \( 0\) , \( -28 i - 21\) , \( 66 i + 12\bigr] \)
32000.2-l7 \( \bigl[0\) , \( 0\) , \( 0\) , \( -8 i - 6\) , \( -11 i - 2\bigr] \)
32000.2-l8 \( \bigl[0\) , \( 0\) , \( 0\) , \( -428 i - 321\) , \( 4686 i + 852\bigr] \)
32000.2-l9 \( \bigl[0\) , \( 0\) , \( 0\) , \( 5332 i + 15999\) , \( 746686 i - 391148\bigr] \)
32000.2-l10 \( \bigl[0\) , \( 0\) , \( 0\) , \( 16852 i + 639\) , \( 561214 i + 628948\bigr] \)

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