Elliptic curve isogeny class 29.4-a over number field 4.4.8000.1

• Base field: 4.4.8000.1
• Label: 4.4.8000.1-29.4-a
• Conductor: 29.4
• 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 29.4-a over 4.4.8000.1

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

Curve label	Weierstrass Coefficients
29.4-a1	\( \bigl[\frac{1}{2} a^{3} - 3 a\) , \( \frac{1}{2} a^{2} - a - 2\) , \( a + 1\) , \( -\frac{7}{2} a^{3} - 6 a^{2} + 24 a + 44\) , \( -\frac{5}{2} a^{3} - 5 a^{2} + 18 a + 33\bigr] \)
29.4-a2	\( \bigl[\frac{1}{2} a^{3} - 2 a\) , \( -\frac{1}{2} a^{3} - \frac{1}{2} a^{2} + 2 a + 3\) , \( 1\) , \( -\frac{7}{2} a^{3} - 3 a^{2} + 11 a + 9\) , \( -6 a^{3} - 11 a^{2} + 17 a + 30\bigr] \)