Properties

Base field 4.4.12400.1
Label 4.4.12400.1-20.2-b
Conductor 20.2
Rank \( 1 \)

Related objects

Learn more about

Base field 4.4.12400.1

Generator \(a\), with minimal polynomial \( x^{4} - 12 x^{2} + 31 \); class number \(1\).

Elliptic curves in class 20.2-b over 4.4.12400.1

Isogeny class 20.2-b contains 2 curves linked by isogenies of degree 3.

Curve label Weierstrass Coefficients
20.2-b1 \( \bigl[a\) , \( \frac{1}{2} a^{3} - \frac{9}{2} a - 1\) , \( \frac{1}{2} a^{3} + \frac{1}{2} a^{2} - \frac{5}{2} a - \frac{5}{2}\) , \( -\frac{1}{2} a^{3} - 4 a^{2} + \frac{5}{2} a + 24\) , \( -\frac{3}{2} a^{2} - 2 a + \frac{9}{2}\bigr] \)
20.2-b2 \( \bigl[\frac{1}{2} a^{3} - \frac{5}{2} a + 1\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - \frac{5}{2} a + \frac{5}{2}\) , \( \frac{1}{2} a^{3} - \frac{5}{2} a + 1\) , \( \frac{31}{2} a^{3} + \frac{87}{2} a^{2} - \frac{117}{2} a - \frac{327}{2}\) , \( -22 a^{3} - 64 a^{2} + 83 a + 241\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph