Properties

Base field 4.4.4752.1
Label 4.4.4752.1-33.1-d
Conductor 33.1
Rank not recorded

Related objects

Learn more about

Base field 4.4.4752.1

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

Elliptic curves in class 33.1-d over 4.4.4752.1

Isogeny class 33.1-d contains 4 curves linked by isogenies of degrees dividing 10.

Curve label Weierstrass Coefficients
33.1-d1 \( \bigl[a^{2} - a - 1\) , \( a^{2} - a - 1\) , \( 1\) , \( 6 a^{2} - 6 a - 17\) , \( -3 a^{2} + 3 a + 14\bigr] \)
33.1-d2 \( \bigl[a^{2} - a - 1\) , \( 1\) , \( a^{2} - a - 2\) , \( -286 a^{2} + 286 a + 34\) , \( 9075 a^{2} - 9075 a - 2342\bigr] \)
33.1-d3 \( \bigl[a^{2} - a - 1\) , \( -a^{2} + a + 3\) , \( 1\) , \( -77 a^{2} + 77 a - 124\) , \( 719 a^{2} - 719 a + 358\bigr] \)
33.1-d4 \( \bigl[a^{2} - a - 1\) , \( -a^{2} + a + 3\) , \( 1\) , \( -7 a^{2} + 7 a + 6\) , \( -12 a^{2} + 12 a + 5\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 5 & 10 & 2 \\ 5 & 1 & 2 & 10 \\ 10 & 2 & 1 & 5 \\ 2 & 10 & 5 & 1 \end{array}\right)\)

Isogeny graph