Properties

Base field 6.6.434581.1
Label 6.6.434581.1-71.2-a
Conductor 71.2
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 71.2-a over 6.6.434581.1

Isogeny class 71.2-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label Weierstrass Coefficients
71.2-a1 \( \bigl[a\) , \( -a^{5} + 2 a^{4} + 4 a^{3} - 4 a^{2} - 4 a + 2\) , \( 3 a^{5} - 7 a^{4} - 8 a^{3} + 15 a^{2} + a - 4\) , \( -5 a^{5} + 14 a^{4} + 8 a^{3} - 25 a^{2} + 6\) , \( a^{5} + a^{4} - 11 a^{3} - a^{2} + 18 a - 8\bigr] \)
71.2-a2 \( \bigl[a^{5} - 2 a^{4} - 4 a^{3} + 5 a^{2} + 4 a - 2\) , \( a^{5} - 4 a^{4} + 10 a^{2} - 2 a - 4\) , \( 3 a^{5} - 6 a^{4} - 10 a^{3} + 12 a^{2} + 5 a - 3\) , \( 11 a^{5} - 15 a^{4} - 45 a^{3} + 17 a^{2} + 18 a - 6\) , \( -14 a^{5} + 9 a^{4} + 66 a^{3} + 31 a^{2} - 27 a - 17\bigr] \)
71.2-a3 \( \bigl[a^{5} - 2 a^{4} - 4 a^{3} + 5 a^{2} + 4 a - 2\) , \( a^{5} - 4 a^{4} + 10 a^{2} - 2 a - 4\) , \( 3 a^{5} - 6 a^{4} - 10 a^{3} + 12 a^{2} + 5 a - 3\) , \( 46 a^{5} - 110 a^{4} - 120 a^{3} + 232 a^{2} + 53 a - 96\) , \( 44 a^{5} - 93 a^{4} - 283 a^{3} + 570 a^{2} + 181 a - 275\bigr] \)
71.2-a4 \( \bigl[a\) , \( -a^{5} + 2 a^{4} + 4 a^{3} - 4 a^{2} - 4 a + 2\) , \( 3 a^{5} - 7 a^{4} - 8 a^{3} + 15 a^{2} + a - 4\) , \( 20 a^{5} - 51 a^{4} - 52 a^{3} + 120 a^{2} + 55 a - 84\) , \( 251 a^{5} - 630 a^{4} - 644 a^{3} + 1463 a^{2} + 269 a - 526\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph