Base field 4.4.725.1
Generator \(a\), with minimal polynomial \( x^{4} - x^{3} - 3 x^{2} + x + 1 \); class number \(1\).
Elliptic curves in class 109.1-b over 4.4.725.1
Isogeny class 109.1-b contains only one elliptic curve.
| Curve label | Weierstrass Coefficients |
|---|---|
| 109.1-b1 | \( \bigl[a^{3} - a^{2} - 2 a + 2\) , \( -a^{2} + 2 a + 1\) , \( a^{2} - a - 1\) , \( 4 a^{3} - 15 a - 8\) , \( -8 a^{3} + 2 a^{2} + 25 a + 8\bigr] \) |
Rank
Rank: \( 0 \)Isogeny matrix
\(\left(\begin{array}{r} 1 \end{array}\right)\)
Isogeny graph
