Properties

Base field 4.4.13968.1
Label 4.4.13968.1-8.2-a
Conductor 8.2
Rank not recorded

Related objects

Learn more about

Base field 4.4.13968.1

Generator \(a\), with minimal polynomial \( x^{4} - 2 x^{3} - 7 x^{2} + 8 x + 4 \); class number \(1\).

Elliptic curves in class 8.2-a over 4.4.13968.1

Isogeny class 8.2-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label Weierstrass Coefficients
8.2-a1 \( \bigl[\frac{1}{2} a^{2} + \frac{1}{2} a - 2\) , \( \frac{1}{2} a^{2} - \frac{3}{2} a - 3\) , \( 0\) , \( -\frac{3}{2} a^{3} + \frac{7}{2} a^{2} + 9 a - 10\) , \( -a^{3} + 3 a^{2} + 5 a - 12\bigr] \)
8.2-a2 \( \bigl[\frac{1}{2} a^{2} + \frac{1}{2} a - 2\) , \( -\frac{1}{2} a^{3} + \frac{1}{2} a^{2} + 4 a - 1\) , \( \frac{1}{2} a^{3} - \frac{5}{2} a\) , \( -\frac{7}{2} a^{3} + 2 a^{2} + \frac{51}{2} a + 7\) , \( -14 a^{3} + 8 a^{2} + 108 a + 39\bigr] \)
8.2-a3 \( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 2 a + 1\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 3\) , \( 0\) , \( a^{3} + 2 a^{2} - 2 a - 3\) , \( 2 a^{3} + a^{2} - 6 a + 1\bigr] \)
8.2-a4 \( \bigl[\frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 2 a + 1\) , \( -1\) , \( a + 1\) , \( 2 a^{3} + \frac{3}{2} a^{2} - \frac{29}{2} a - 19\) , \( \frac{29}{2} a^{3} - 10 a^{2} - \frac{213}{2} a - 20\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph