Properties

Base field 4.4.4752.1
Label 4.4.4752.1-39.1-d
Conductor 39.1
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 39.1-d over 4.4.4752.1

Isogeny class 39.1-d contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
39.1-d1 \( \bigl[a^{3} - 4 a - 1\) , \( a^{3} - a^{2} - 2 a + 1\) , \( a^{3} - a^{2} - 2 a + 1\) , \( a^{3} + a^{2} - 3 a + 1\) , \( a^{3} - a\bigr] \)
39.1-d2 \( \bigl[a^{3} - a^{2} - 3 a + 2\) , \( -a^{3} + a^{2} + 4 a - 2\) , \( a^{2} - 1\) , \( -4 a^{3} + 6 a^{2} + 10 a - 11\) , \( 2 a^{3} - 6 a^{2} - 5 a + 12\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph