Properties

Base field 6.6.434581.1
Label 6.6.434581.1-27.1-a
Conductor 27.1
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 27.1-a over 6.6.434581.1

Isogeny class 27.1-a contains 2 curves linked by isogenies of degree 3.

Curve label Weierstrass Coefficients
27.1-a1 \( \bigl[a^{5} - 2 a^{4} - 3 a^{3} + 4 a^{2}\) , \( -a^{4} + a^{3} + 5 a^{2} - 3\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 3 a + 2\) , \( 8 a^{5} - 6 a^{4} - 38 a^{3} - 10 a^{2} + 16 a + 6\) , \( 69 a^{5} - 47 a^{4} - 338 a^{3} - 101 a^{2} + 144 a + 52\bigr] \)
27.1-a2 \( \bigl[3 a^{5} - 6 a^{4} - 10 a^{3} + 12 a^{2} + 4 a - 3\) , \( a^{5} - 4 a^{4} + 10 a^{2} - a - 4\) , \( 2 a^{5} - 5 a^{4} - 5 a^{3} + 11 a^{2} + 2 a - 2\) , \( -10 a^{5} + 13 a^{4} + 41 a^{3} - 9 a^{2} - 18 a + 1\) , \( -10 a^{5} + 10 a^{4} + 46 a^{3} - a^{2} - 20 a - 2\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph