Elliptic curve isogeny class 29.1-a over number field 4.4.8000.1

• Base field: 4.4.8000.1
• Label: 4.4.8000.1-29.1-a
• Number of curves: 2
• Conductor: 29.1
• 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 29.1-a over 4.4.8000.1

Isogeny class 29.1-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
29.1-a1	\( \bigl[\frac{1}{2} a^{3} - 3 a\) , \( \frac{1}{2} a^{2} + a - 2\) , \( a + 1\) , \( 3 a^{3} - 6 a^{2} - 21 a + 44\) , \( \frac{5}{2} a^{3} - 5 a^{2} - 19 a + 33\bigr] \)
29.1-a2	\( \bigl[\frac{1}{2} a^{3} - 2 a\) , \( \frac{1}{2} a^{3} - \frac{1}{2} a^{2} - 2 a + 3\) , \( 1\) , \( 3 a^{3} - 3 a^{2} - 9 a + 9\) , \( 6 a^{3} - 11 a^{2} - 17 a + 30\bigr] \)