Elliptic curve isogeny class 29.2-b over number field 4.4.19821.1

• Base field: 4.4.19821.1
• Label: 4.4.19821.1-29.2-b
• Conductor: 29.2
• Rank: \( 1 \)

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 29.2-b over 4.4.19821.1

Isogeny class 29.2-b contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
29.2-b1	\( \bigl[-\frac{1}{3} a^{3} + \frac{2}{3} a^{2} + 3 a - 3\) , \( \frac{2}{3} a^{3} - \frac{1}{3} a^{2} - 4 a + 2\) , \( 0\) , \( \frac{2}{3} a^{3} - \frac{7}{3} a^{2} - 8 a + 10\) , \( -7 a^{3} - 15 a^{2} + 15 a + 13\bigr] \)
29.2-b2	\( \bigl[\frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 3 a - 1\) , \( \frac{1}{3} a^{3} - \frac{2}{3} a^{2} - 2 a + 4\) , \( \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 2 a - 1\) , \( -2 a^{3} - a^{2} + 10 a - 5\) , \( -\frac{20}{3} a^{3} + \frac{1}{3} a^{2} + 37 a - 31\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph