Properties

Base field 4.4.2777.1
Label 4.4.2777.1-16.1-a
Conductor 16.1
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 16.1-a over 4.4.2777.1

Isogeny class 16.1-a contains 8 curves linked by isogenies of degrees dividing 12.

Curve label Weierstrass Coefficients
16.1-a1 \( \bigl[a^{3} - 4 a - 1\) , \( -a^{3} + a^{2} + 3 a - 1\) , \( a^{3} - a^{2} - 3 a + 2\) , \( -27 a^{3} + 35 a^{2} + 72 a - 62\) , \( -75 a^{3} + 102 a^{2} + 199 a - 190\bigr] \)
16.1-a2 \( \bigl[a^{3} - 4 a - 1\) , \( -a^{3} + a^{2} + 3 a - 1\) , \( a^{3} - a^{2} - 3 a + 2\) , \( -2 a^{3} + 7 a + 3\) , \( -2 a^{3} + 2 a^{2} + 7 a - 1\bigr] \)
16.1-a3 \( \bigl[a^{3} - 3 a - 1\) , \( -a - 1\) , \( a^{3} - a^{2} - 2 a + 2\) , \( -11 a^{3} - 17 a^{2} + 2 a + 4\) , \( 56 a^{3} + 79 a^{2} - 40 a - 48\bigr] \)
16.1-a4 \( \bigl[1\) , \( -a^{3} + 2 a^{2} + 2 a - 3\) , \( a^{3} - 4 a\) , \( 248 a^{3} + 94 a^{2} - 178 a - 86\) , \( -61 a^{3} + 1602 a^{2} - 240 a - 924\bigr] \)
16.1-a5 \( \bigl[1\) , \( a^{3} - a^{2} - 4 a + 1\) , \( a^{2} - 2\) , \( 110 a^{3} - 287 a^{2} + 7 a + 128\) , \( -927 a^{3} + 2286 a^{2} + 326 a - 1304\bigr] \)
16.1-a6 \( \bigl[a + 1\) , \( a^{2} - a - 1\) , \( 0\) , \( 42 a^{3} - 3 a^{2} - 178 a - 115\) , \( 260 a^{3} - 47 a^{2} - 1076 a - 623\bigr] \)
16.1-a7 \( \bigl[a + 1\) , \( a^{3} - a^{2} - 3 a\) , \( a^{3} - a^{2} - 2 a + 1\) , \( 30 a^{3} - 52 a^{2} - 65 a - 13\) , \( 91 a^{3} - 127 a^{2} - 206 a - 56\bigr] \)
16.1-a8 \( \bigl[a + 1\) , \( a^{3} - a^{2} - 3 a\) , \( a^{3} - a^{2} - 2 a + 1\) , \( 230 a^{3} - 692 a^{2} - 65 a + 307\) , \( 4699 a^{3} - 10439 a^{2} - 1286 a + 5304\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 3 & 6 & 4 & 12 & 12 & 2 & 4 \\ 3 & 1 & 2 & 12 & 4 & 4 & 6 & 12 \\ 6 & 2 & 1 & 6 & 2 & 2 & 3 & 6 \\ 4 & 12 & 6 & 1 & 12 & 3 & 2 & 4 \\ 12 & 4 & 2 & 12 & 1 & 4 & 6 & 3 \\ 12 & 4 & 2 & 3 & 4 & 1 & 6 & 12 \\ 2 & 6 & 3 & 2 & 6 & 6 & 1 & 2 \\ 4 & 12 & 6 & 4 & 3 & 12 & 2 & 1 \end{array}\right)\)

Isogeny graph