Properties

Base field 6.6.434581.1
Label 6.6.434581.1-29.1-a
Conductor 29.1
Rank not recorded

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Base field 6.6.434581.1

Generator \(a\), with minimal polynomial \( x^{6} - 2 x^{5} - 4 x^{4} + 5 x^{3} + 4 x^{2} - 2 x - 1 \); class number \(1\).

Elliptic curves in class 29.1-a over 6.6.434581.1

Isogeny class 29.1-a contains 4 curves linked by isogenies of degrees dividing 15.

Curve label Weierstrass Coefficients
29.1-a1 \( \bigl[a^{5} - a^{4} - 5 a^{3} + a^{2} + 4 a + 1\) , \( -a^{3} + 2 a^{2} + a - 3\) , \( 3 a^{5} - 6 a^{4} - 10 a^{3} + 12 a^{2} + 5 a - 2\) , \( -34 a^{5} + 81 a^{4} + 65 a^{3} - 117 a^{2} - 27 a + 6\) , \( -56 a^{5} + 163 a^{4} + 31 a^{3} - 264 a^{2} - 13 a + 30\bigr] \)
29.1-a2 \( \bigl[3 a^{5} - 6 a^{4} - 10 a^{3} + 12 a^{2} + 5 a - 2\) , \( -a^{4} + 2 a^{3} + 3 a^{2} - 3 a - 1\) , \( 2 a^{5} - 4 a^{4} - 6 a^{3} + 7 a^{2} + a - 1\) , \( -25 a^{5} + 65 a^{4} + 75 a^{3} - 170 a^{2} - 65 a + 5\) , \( -81 a^{5} + 262 a^{4} + 173 a^{3} - 737 a^{2} - 174 a + 41\bigr] \)
29.1-a3 \( \bigl[3 a^{5} - 6 a^{4} - 10 a^{3} + 12 a^{2} + 4 a - 2\) , \( a^{5} - 3 a^{4} - a^{3} + 7 a^{2} - 2 a - 2\) , \( a^{5} - 2 a^{4} - 3 a^{3} + 4 a^{2} - 1\) , \( -29 a^{5} + 67 a^{4} + 95 a^{3} - 175 a^{2} - 56 a + 79\) , \( -60 a^{5} + 141 a^{4} + 189 a^{3} - 364 a^{2} - 105 a + 158\bigr] \)
29.1-a4 \( \bigl[3 a^{5} - 6 a^{4} - 10 a^{3} + 12 a^{2} + 5 a - 2\) , \( -a^{4} + 2 a^{3} + 3 a^{2} - 3 a - 1\) , \( 2 a^{5} - 4 a^{4} - 6 a^{3} + 7 a^{2} + a - 1\) , \( 0\) , \( 0\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 5 & 15 \\ 3 & 1 & 15 & 5 \\ 5 & 15 & 1 & 3 \\ 15 & 5 & 3 & 1 \end{array}\right)\)

Isogeny graph