Elliptic curve isogeny class 29.2-d over number field 6.6.434581.1

• Base field: 6.6.434581.1
• Label: 6.6.434581.1-29.2-d
• Conductor: 29.2
• Rank: \( 1 \)

Base field 6.6.434581.1

Generator \(a\), with minimal polynomial \( x^{6} - 2 x^{5} - 4 x^{4} + 5 x^{3} + 4 x^{2} - 2 x - 1 \); class number \(1\).

Elliptic curves in class 29.2-d over 6.6.434581.1

Isogeny class 29.2-d contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
29.2-d1	\( \bigl[a^{5} - a^{4} - 5 a^{3} + a^{2} + 3 a\) , \( -2 a^{5} + 4 a^{4} + 7 a^{3} - 8 a^{2} - 5 a + 2\) , \( 3 a^{5} - 6 a^{4} - 10 a^{3} + 12 a^{2} + 5 a - 2\) , \( -a^{5} + 5 a^{3} + 6 a^{2} - 2 a - 3\) , \( -4 a^{5} + 4 a^{4} + 18 a^{3} + a^{2} - 8 a - 3\bigr] \)
29.2-d2	\( \bigl[a^{5} - a^{4} - 5 a^{3} + a^{2} + 3 a + 1\) , \( -a^{5} + 2 a^{4} + 4 a^{3} - 4 a^{2} - 5 a + 2\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 3 a + 2\) , \( a^{4} - 3 a^{3} - 2 a^{2} + 3 a + 5\) , \( a^{5} - 8 a^{3} - a^{2} + 9 a + 5\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph