Properties

Base field 4.4.7168.1
Label 4.4.7168.1-32.1-b
Conductor 32.1
Rank \( 1 \)

Related objects

Learn more about

Base field 4.4.7168.1

Generator \(a\), with minimal polynomial \( x^{4} - 6 x^{2} + 7 \); class number \(1\).

Elliptic curves in class 32.1-b over 4.4.7168.1

Isogeny class 32.1-b contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
32.1-b1 \( \bigl[a^{3} + a^{2} - 3 a - 3\) , \( a^{3} - a^{2} - 3 a + 2\) , \( 0\) , \( 13 a^{3} - 24 a^{2} - 21 a + 39\) , \( -79 a^{3} + 168 a^{2} + 125 a - 266\bigr] \)
32.1-b2 \( \bigl[a^{3} + a^{2} - 3 a - 3\) , \( -a^{3} + 4 a\) , \( 0\) , \( -3 a^{2} + 4 a + 10\) , \( -17 a^{3} + 34 a^{2} + 28 a - 49\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph