Properties

Base field 6.6.434581.1
Label 6.6.434581.1-71.1-a
Conductor 71.1
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 71.1-a over 6.6.434581.1

Isogeny class 71.1-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label Weierstrass Coefficients
71.1-a1 \( \bigl[a^{5} - 3 a^{4} - 2 a^{3} + 8 a^{2} + a - 2\) , \( 2 a^{5} - 4 a^{4} - 7 a^{3} + 9 a^{2} + 2 a - 3\) , \( 2 a^{5} - 4 a^{4} - 6 a^{3} + 7 a^{2} + 2 a - 1\) , \( 3 a^{5} - 10 a^{4} - 6 a^{3} + 31 a^{2} + 3 a - 14\) , \( 4 a^{5} - 9 a^{4} - 13 a^{3} + 22 a^{2} + 7 a - 10\bigr] \)
71.1-a2 \( \bigl[a^{5} - 2 a^{4} - 4 a^{3} + 5 a^{2} + 4 a - 1\) , \( -a^{5} + 6 a^{3} + 4 a^{2} - 3 a - 2\) , \( 0\) , \( -4 a^{5} + 3 a^{4} + 19 a^{3} + 5 a^{2} - 7 a - 2\) , \( 0\bigr] \)
71.1-a3 \( \bigl[a^{5} - 2 a^{4} - 4 a^{3} + 5 a^{2} + 3 a - 2\) , \( a^{5} - 3 a^{4} - a^{3} + 6 a^{2} - 3 a - 2\) , \( 2 a^{5} - 4 a^{4} - 6 a^{3} + 7 a^{2} + 2 a - 1\) , \( 10 a^{5} - 30 a^{4} - 10 a^{3} + 51 a^{2} - a - 14\) , \( -15 a^{5} + 55 a^{4} - 31 a^{3} - 39 a^{2} + 17 a + 6\bigr] \)
71.1-a4 \( \bigl[a^{5} - 2 a^{4} - 3 a^{3} + 3 a^{2} + a + 1\) , \( -2 a^{5} + 5 a^{4} + 5 a^{3} - 11 a^{2} - a + 2\) , \( a^{5} - 2 a^{4} - 3 a^{3} + 3 a^{2} + a\) , \( -97 a^{5} + 157 a^{4} + 417 a^{3} - 259 a^{2} - 387 a - 94\) , \( -599 a^{5} + 877 a^{4} + 2755 a^{3} - 1288 a^{2} - 2719 a - 723\bigr] \)

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