Elliptic curve isogeny class 29.3-a over number field 4.4.8000.1

• Base field: 4.4.8000.1
• Label: 4.4.8000.1-29.3-a
• Conductor: 29.3
• Rank: \( 0 \)

Base field 4.4.8000.1

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

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph

Elliptic curves in class 29.3-a over 4.4.8000.1

Isogeny class 29.3-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
29.3-a1	\( \bigl[\frac{1}{2} a^{3} - 2 a\) , \( -\frac{1}{2} a^{3} + 4 a - 1\) , \( a + 1\) , \( -3 a^{3} + \frac{7}{2} a^{2} + 22 a - 27\) , \( -3 a^{3} + 5 a^{2} + 22 a - 37\bigr] \)
29.3-a2	\( \bigl[a\) , \( -\frac{1}{2} a^{3} - \frac{1}{2} a^{2} + 3 a + 3\) , \( \frac{1}{2} a^{3} - 3 a + 1\) , \( \frac{3}{2} a^{3} + 4 a^{2} - 3 a - 6\) , \( \frac{3}{2} a^{3} + 5 a^{2} - 4 a - 17\bigr] \)