Properties

Base field 4.4.19821.1
Label 4.4.19821.1-27.2-f
Conductor 27.2
Rank not recorded

Related objects

Learn more about

Base field 4.4.19821.1

Generator \(a\), with minimal polynomial \( x^{4} - x^{3} - 8 x^{2} + 6 x + 3 \); class number \(1\).

Elliptic curves in class 27.2-f over 4.4.19821.1

Isogeny class 27.2-f contains 2 curves linked by isogenies of degree 3.

Curve label Weierstrass Coefficients
27.2-f1 \( \bigl[-\frac{1}{3} a^{3} + \frac{2}{3} a^{2} + 3 a - 3\) , \( -\frac{1}{3} a^{3} + \frac{2}{3} a^{2} + 3 a - 2\) , \( \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 2 a - 1\) , \( \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 2 a - 1\) , \( 0\bigr] \)
27.2-f2 \( \bigl[-\frac{1}{3} a^{3} + \frac{2}{3} a^{2} + 3 a - 3\) , \( -\frac{1}{3} a^{3} + \frac{2}{3} a^{2} + 3 a - 2\) , \( \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 2 a - 1\) , \( -\frac{19}{3} a^{3} - \frac{19}{3} a^{2} + 33 a + 9\) , \( -\frac{67}{3} a^{3} - \frac{124}{3} a^{2} + 59 a + 22\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

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

Isogeny graph