Properties

Base field 4.4.6809.1
Label 4.4.6809.1-8.1-a
Conductor 8.1
Rank \( 1 \)

Related objects

Learn more about

Base field 4.4.6809.1

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

Elliptic curves in class 8.1-a over 4.4.6809.1

Isogeny class 8.1-a contains only one elliptic curve.

Curve label Weierstrass Coefficients
8.1-a1 \( \bigl[a^{2} - 2\) , \( -a^{3} + a^{2} + 5 a - 1\) , \( a^{2} + a - 2\) , \( 3 a^{3} - 6 a^{2} - a + 2\) , \( -6 a^{3} + 12 a^{2} + 6 a - 3\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{r} 1 \end{array}\right)\)

Isogeny graph