Properties

Base field 6.6.434581.1
Label 6.6.434581.1-43.1-a
Conductor 43.1
Rank not recorded

Related objects

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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 43.1-a over 6.6.434581.1

Isogeny class 43.1-a contains 2 curves linked by isogenies of degree 3.

Curve label Weierstrass Coefficients
43.1-a1 \( \bigl[2 a^{5} - 4 a^{4} - 7 a^{3} + 9 a^{2} + 3 a - 3\) , \( a^{5} - 2 a^{4} - 2 a^{3} + 2 a^{2} - 2 a + 2\) , \( 2 a^{5} - 3 a^{4} - 8 a^{3} + 4 a^{2} + 5 a + 1\) , \( -a^{5} + 3 a^{4} + 5 a^{3} - 12 a^{2} - 9 a + 6\) , \( -2 a^{5} + 5 a^{4} + 5 a^{3} - 15 a^{2} - 3 a + 5\bigr] \)
43.1-a2 \( \bigl[2 a^{5} - 4 a^{4} - 7 a^{3} + 8 a^{2} + 5 a - 1\) , \( a^{5} - 3 a^{4} - 2 a^{3} + 8 a^{2} + a - 2\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 4 a + 2\) , \( 7 a^{5} - 17 a^{4} - 23 a^{3} + 48 a^{2} + 15 a - 22\) , \( 11 a^{5} - 24 a^{4} - 37 a^{3} + 66 a^{2} + 25 a - 32\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

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

Isogeny graph