Elliptic curve isogeny class 29.4-b over number field 4.4.8000.1

• Base field: 4.4.8000.1
• Label: 4.4.8000.1-29.4-b
• Conductor: 29.4
• Rank: \( 1 \)

Base field 4.4.8000.1

Generator \(a\), with minimal polynomial \( x^{4} - 10 x^{2} + 20 \); class number \(1\).

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

Elliptic curves in class 29.4-b over 4.4.8000.1

Isogeny class 29.4-b contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
29.4-b1	\( \bigl[\frac{1}{2} a^{3} - 3 a\) , \( \frac{1}{2} a^{2} - a - 2\) , \( \frac{1}{2} a^{3} - 2 a + 1\) , \( \frac{7}{2} a^{3} + \frac{9}{2} a^{2} - 25 a - 38\) , \( \frac{5}{2} a^{3} + \frac{7}{2} a^{2} - 19 a - 30\bigr] \)
29.4-b2	\( \bigl[\frac{1}{2} a^{3} - 2 a\) , \( -\frac{1}{2} a^{3} - \frac{1}{2} a^{2} + 2 a + 3\) , \( \frac{1}{2} a^{3} - 3 a + 1\) , \( -a^{3} + 3 a^{2} + 4 a - 8\) , \( \frac{3}{2} a^{3} + 10 a^{2} - 3 a - 29\bigr] \)