Properties

Base field 6.6.434581.1
Label 6.6.434581.1-29.2-a
Conductor 29.2
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 29.2-a over 6.6.434581.1

Isogeny class 29.2-a contains 4 curves linked by isogenies of degrees dividing 15.

Curve label Weierstrass Coefficients
29.2-a1 \( \bigl[a^{5} - 2 a^{4} - 3 a^{3} + 4 a^{2} + a\) , \( a^{4} - 2 a^{3} - 2 a^{2} + 3 a + 1\) , \( a^{5} - 2 a^{4} - 4 a^{3} + 5 a^{2} + 4 a - 2\) , \( 105 a^{5} - 194 a^{4} - 403 a^{3} + 388 a^{2} + 317 a - 39\) , \( 274 a^{5} - 510 a^{4} - 1086 a^{3} + 1108 a^{2} + 922 a - 292\bigr] \)
29.2-a2 \( \bigl[a^{5} - a^{4} - 5 a^{3} + 5 a + 1\) , \( -a^{5} + 3 a^{4} + 2 a^{3} - 8 a^{2} - a + 3\) , \( a^{5} - 2 a^{4} - 3 a^{3} + 4 a^{2} - 1\) , \( 130 a^{5} - 309 a^{4} - 397 a^{3} + 796 a^{2} + 211 a - 347\) , \( 980 a^{5} - 2356 a^{4} - 3009 a^{3} + 6089 a^{2} + 1599 a - 2603\bigr] \)
29.2-a3 \( \bigl[2 a^{5} - 5 a^{4} - 5 a^{3} + 11 a^{2} + 2 a - 3\) , \( a^{5} - 2 a^{4} - 4 a^{3} + 5 a^{2} + 3 a - 3\) , \( 3 a^{5} - 7 a^{4} - 8 a^{3} + 15 a^{2} + a - 4\) , \( -4 a^{5} + 8 a^{4} + 14 a^{3} - 15 a^{2} - 9 a - 1\) , \( 2 a^{5} - a^{4} - 13 a^{3} - 2 a^{2} + 15 a + 4\bigr] \)
29.2-a4 \( \bigl[3 a^{5} - 7 a^{4} - 8 a^{3} + 15 a^{2} + 2 a - 4\) , \( -a^{4} + 2 a^{3} + 3 a^{2} - 3 a - 1\) , \( 3 a^{5} - 7 a^{4} - 8 a^{3} + 15 a^{2} + a - 3\) , \( 0\) , \( 0\bigr] \)

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