Elliptic curve isogeny class 29.2-b over number field 4.4.8000.1

• Base field: 4.4.8000.1
• Label: 4.4.8000.1-29.2-b
• Number of curves: 2
• Conductor: 29.2
• 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 29.2-b over 4.4.8000.1

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

Curve label	Weierstrass Coefficients
29.2-b1	\( \bigl[\frac{1}{2} a^{3} - 2 a\) , \( \frac{1}{2} a^{3} - 4 a - 1\) , \( 1\) , \( -\frac{3}{2} a^{3} - \frac{3}{2} a^{2} + 9 a + 16\) , \( -3 a^{3} - \frac{9}{2} a^{2} + 21 a + 35\bigr] \)
29.2-b2	\( \bigl[a\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 3 a + 3\) , \( \frac{1}{2} a^{3} - 2 a + 1\) , \( 2 a^{3} - \frac{13}{2} a^{2} - 5 a + 17\) , \( \frac{3}{2} a^{3} - \frac{11}{2} a^{2} - 4 a + 15\bigr] \)