Elliptic curve isogeny class 29.1-a over number field 6.6.966125.1

• Base field: 6.6.966125.1
• Label: 6.6.966125.1-29.1-a
• Conductor: 29.1
• Rank: \( 1 \)

Base field 6.6.966125.1

Generator \(a\), with minimal polynomial \( x^{6} - x^{5} - 6 x^{4} + 4 x^{3} + 8 x^{2} - 1 \); class number \(1\).

Elliptic curves in class 29.1-a over 6.6.966125.1

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

Curve label	Weierstrass Coefficients
29.1-a1	\( \bigl[a^{5} - a^{4} - 5 a^{3} + 4 a^{2} + 4 a\) , \( -a^{5} + a^{4} + 4 a^{3} - 4 a^{2} - a - 1\) , \( a^{5} - 2 a^{4} - 5 a^{3} + 9 a^{2} + 5 a - 2\) , \( -4 a^{5} + 8 a^{4} + 18 a^{3} - 33 a^{2} - 6 a + 5\) , \( 217 a^{5} - 402 a^{4} - 960 a^{3} + 1685 a^{2} + 300 a - 255\bigr] \)
29.1-a2	\( \bigl[1\) , \( a^{5} - a^{4} - 6 a^{3} + 5 a^{2} + 9 a - 3\) , \( a^{5} - 2 a^{4} - 5 a^{3} + 9 a^{2} + 4 a - 2\) , \( -48 a^{5} + 100 a^{4} + 217 a^{3} - 427 a^{2} - 83 a + 68\) , \( 360 a^{5} - 685 a^{4} - 1597 a^{3} + 2888 a^{2} + 509 a - 437\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph