Properties

Base field 3.3.316.1
Label 3.3.316.1-16.1-a
Conductor 16.1
Rank \( 0 \)

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Base field 3.3.316.1

Generator \(a\), with minimal polynomial \( x^{3} - x^{2} - 4 x + 2 \); class number \(1\).

Elliptic curves in class 16.1-a over 3.3.316.1

Isogeny class 16.1-a contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
16.1-a1 \( \bigl[a^{2} - 2\) , \( a^{2} - a - 3\) , \( a^{2} - 2\) , \( -3 a^{2} + 2 a + 9\) , \( -2 a^{2} + 3 a + 2\bigr] \)
16.1-a2 \( \bigl[a\) , \( a^{2} + a - 4\) , \( 0\) , \( 89717 a^{2} - 47509 a - 381256\) , \( -21491631 a^{2} + 11375920 a + 91321039\bigr] \)
16.1-a3 \( \bigl[a\) , \( a^{2} + a - 4\) , \( 0\) , \( 5607 a^{2} - 2969 a - 23826\) , \( -340349 a^{2} + 180146 a + 1446179\bigr] \)
16.1-a4 \( \bigl[a\) , \( a^{2} - 2\) , \( a^{2} - 2\) , \( 49623936 a^{2} - 26266736 a - 210859010\) , \( -374288977427 a^{2} + 198117361452 a + 1590406466852\bigr] \)
16.1-a5 \( \bigl[a\) , \( -a\) , \( a^{2} - 2\) , \( -a^{2} - a + 1\) , \( -a^{2} + a - 1\bigr] \)
16.1-a6 \( \bigl[a\) , \( -a\) , \( a^{2} - 2\) , \( -6 a^{2} - 11 a + 6\) , \( -16 a^{2} - 18 a + 11\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph