Properties

Base field 6.6.434581.1
Label 6.6.434581.1-71.2-b
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-b over 6.6.434581.1

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

Curve label Weierstrass Coefficients
71.2-b1 \( \bigl[2 a^{5} - 4 a^{4} - 7 a^{3} + 9 a^{2} + 3 a - 3\) , \( 2 a^{5} - 5 a^{4} - 5 a^{3} + 11 a^{2} - 4\) , \( a^{5} - 2 a^{4} - 4 a^{3} + 5 a^{2} + 4 a - 1\) , \( 10 a^{5} - 30 a^{4} - 16 a^{3} + 72 a^{2} - 2 a - 32\) , \( a^{5} + 3 a^{4} - 24 a^{3} + 25 a^{2} + 18 a - 26\bigr] \)
71.2-b2 \( \bigl[a^{5} - 2 a^{4} - 4 a^{3} + 5 a^{2} + 4 a - 2\) , \( -2 a^{5} + 4 a^{4} + 7 a^{3} - 8 a^{2} - 5 a + 1\) , \( a^{5} - 2 a^{4} - 3 a^{3} + 4 a^{2} + a - 1\) , \( 3 a^{5} - 5 a^{4} - 12 a^{3} + 9 a^{2} + 7 a - 2\) , \( 6 a^{5} - 16 a^{4} - 17 a^{3} + 45 a^{2} + 9 a - 20\bigr] \)
71.2-b3 \( \bigl[a^{5} - a^{4} - 5 a^{3} + 5 a + 1\) , \( -3 a^{5} + 6 a^{4} + 10 a^{3} - 12 a^{2} - 5 a + 3\) , \( a^{5} - 2 a^{4} - 3 a^{3} + 4 a^{2} - 1\) , \( -2 a^{5} + 3 a^{4} + 8 a^{3} - 4 a^{2} - 5 a + 2\) , \( -a^{5} + 2 a^{4} + 3 a^{3} - 4 a^{2} + 2\bigr] \)
71.2-b4 \( \bigl[a^{5} - a^{4} - 5 a^{3} + 5 a + 1\) , \( -3 a^{5} + 6 a^{4} + 10 a^{3} - 12 a^{2} - 5 a + 3\) , \( a^{5} - 2 a^{4} - 3 a^{3} + 4 a^{2} - 1\) , \( -2 a^{5} + 3 a^{4} + 13 a^{3} - 9 a^{2} - 25 a - 8\) , \( 11 a^{5} - 17 a^{4} - 50 a^{3} + 24 a^{2} + 58 a + 16\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

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

Isogeny graph