Properties

Base field 4.4.2777.1
Label 4.4.2777.1-11.1-a
Conductor 11.1
Rank not recorded

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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 11.1-a over 4.4.2777.1

Isogeny class 11.1-a contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
11.1-a1 \( \bigl[a^{3} - 4 a - 1\) , \( -1\) , \( a^{3} - 4 a\) , \( 5 a^{3} - 14 a^{2} + 3 a + 1\) , \( -16 a^{3} + 40 a^{2} - 7 a - 14\bigr] \)
11.1-a2 \( \bigl[a^{3} - 3 a - 1\) , \( a^{2} - 3\) , \( a^{3} - a^{2} - 3 a + 2\) , \( a^{3} + 2 a^{2} - a - 1\) , \( a^{3} + 3 a^{2} - 4\bigr] \)
11.1-a3 \( \bigl[a^{3} - a^{2} - 3 a + 1\) , \( -a\) , \( a^{2} - a - 1\) , \( -2 a^{2} - a + 1\) , \( -2 a^{2} + 1\bigr] \)
11.1-a4 \( \bigl[a^{3} - a^{2} - 3 a + 1\) , \( -a\) , \( a^{2} - a - 1\) , \( -5 a^{3} - 27 a^{2} + 4 a + 16\) , \( -36 a^{3} - 102 a^{2} + 35 a + 61\bigr] \)
11.1-a5 \( \bigl[1\) , \( -a^{3} + 3 a\) , \( a^{2} - 1\) , \( -68 a^{3} + 158 a^{2} + 160 a - 355\) , \( 927 a^{3} - 1319 a^{2} - 2859 a + 1883\bigr] \)
11.1-a6 \( \bigl[1\) , \( -a^{3} + 3 a\) , \( a^{2} - 1\) , \( -3 a^{3} + 8 a^{2} + 10 a - 20\) , \( 16 a^{3} - 23 a^{2} - 54 a + 33\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

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

Isogeny graph