Properties

Base field 5.5.65657.1
Label 5.5.65657.1-43.1-a
Conductor 43.1
Rank not recorded

Related objects

Learn more about

Base field 5.5.65657.1

Generator \(a\), with minimal polynomial \( x^{5} - x^{4} - 5 x^{3} + 2 x^{2} + 5 x + 1 \); class number \(1\).

Elliptic curves in class 43.1-a over 5.5.65657.1

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

Curve label Weierstrass Coefficients
43.1-a1 \( \bigl[1\) , \( -2 a^{4} + 3 a^{3} + 9 a^{2} - 10 a - 8\) , \( a^{4} - a^{3} - 4 a^{2} + 3 a + 2\) , \( -a^{4} - 2 a^{3} + 4 a^{2} + 11 a + 10\) , \( 2 a^{4} + 3 a^{3} - 9 a^{2} - 20 a - 9\bigr] \)
43.1-a2 \( \bigl[-2 a^{4} + 3 a^{3} + 9 a^{2} - 8 a - 6\) , \( a^{4} - 2 a^{3} - 4 a^{2} + 7 a + 2\) , \( a + 1\) , \( 5 a^{4} - 3 a^{3} - 21 a^{2} - 3 a + 6\) , \( 9 a^{4} + 2 a^{3} - 40 a^{2} - 33 a - 4\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

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

Isogeny graph