Properties

Base field 4.4.2777.1
Label 4.4.2777.1-16.2-a
Conductor 16.2
Rank not recorded

Related objects

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Base field 4.4.2777.1

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

Elliptic curves in class 16.2-a over 4.4.2777.1

Isogeny class 16.2-a contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
16.2-a1 \( \bigl[a^{3} - 4 a\) , \( -a + 1\) , \( a^{3} - a^{2} - 2 a + 2\) , \( -6 a^{3} + 12 a^{2} + 12 a - 24\) , \( 9 a^{3} - 10 a^{2} - 32 a + 7\bigr] \)
16.2-a2 \( \bigl[a^{3} - 4 a\) , \( -a^{2} + 1\) , \( a^{2} - a - 2\) , \( -76 a^{3} + 192 a^{2} + 10 a - 99\) , \( 264 a^{3} - 660 a^{2} - 64 a + 352\bigr] \)
16.2-a3 \( \bigl[a^{3} - 3 a\) , \( -a^{3} + 3 a + 2\) , \( a^{3} - 3 a\) , \( -2 a^{3} + 6 a + 2\) , \( -a^{3} + 3 a + 1\bigr] \)
16.2-a4 \( \bigl[a\) , \( -a^{2} + a + 2\) , \( a^{3} - a^{2} - 3 a + 2\) , \( 36 a^{3} - 6 a^{2} - 152 a - 92\) , \( -24 a^{3} - 4 a^{2} + 80 a + 48\bigr] \)
16.2-a5 \( \bigl[a^{3} - a^{2} - 3 a + 2\) , \( -a^{3} + a^{2} + 2 a - 2\) , \( a\) , \( -4 a^{3} + 16 a^{2} - 4 a - 67\) , \( -8 a^{3} + 53 a^{2} - 21 a - 199\bigr] \)
16.2-a6 \( \bigl[a^{3} - a^{2} - 3 a + 2\) , \( -a^{3} + a^{2} + 2 a - 2\) , \( a\) , \( -4 a^{3} + a^{2} + 6 a - 7\) , \( -9 a^{2} - 7 a + 9\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

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

Isogeny graph