Properties

Base field 3.3.733.1
Label 3.3.733.1-8.1-b
Conductor 8.1
Rank not recorded

Related objects

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Base field 3.3.733.1

Generator \(a\), with minimal polynomial \( x^{3} - x^{2} - 7 x + 8 \); class number \(1\).

Elliptic curves in class 8.1-b over 3.3.733.1

Isogeny class 8.1-b contains 4 curves linked by isogenies of degrees dividing 6.

Curve label Weierstrass Coefficients
8.1-b1 \( \bigl[1\) , \( a^{2} - 6\) , \( a + 1\) , \( -3206 a^{2} + 11846 a - 9503\) , \( -315543 a^{2} + 1166369 a - 936192\bigr] \)
8.1-b2 \( \bigl[1\) , \( a^{2} - 6\) , \( a + 1\) , \( -46 a^{2} + 166 a - 128\) , \( -325 a^{2} + 1200 a - 964\bigr] \)
8.1-b3 \( \bigl[1\) , \( -a + 1\) , \( a^{2} - 4\) , \( 398163 a^{2} + 83660 a - 2735554\) , \( -225568877 a^{2} - 41410904 a + 1534686372\bigr] \)
8.1-b4 \( \bigl[1\) , \( -a + 1\) , \( a^{2} - 4\) , \( -1508637 a^{2} - 142020 a + 9924391\) , \( -1132431610 a^{2} - 162413806 a + 7590106761\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph