Elliptic curve isogeny class 29.1-a over number field 6.6.1241125.1

• Base field: 6.6.1241125.1
• Label: 6.6.1241125.1-29.1-a
• Conductor: 29.1
• Rank: \( 1 \)

Base field 6.6.1241125.1

Generator \(a\), with minimal polynomial \( x^{6} - 7 x^{4} - 2 x^{3} + 11 x^{2} + 7 x + 1 \); class number \(1\).

Elliptic curves in class 29.1-a over 6.6.1241125.1

Isogeny class 29.1-a contains 2 curves linked by isogenies of degree 7.

Curve label	Weierstrass Coefficients
29.1-a1	\( \bigl[a^{2} - 3\) , \( -2 a^{5} + a^{4} + 13 a^{3} - 2 a^{2} - 19 a - 5\) , \( -a^{5} + a^{4} + 6 a^{3} - 3 a^{2} - 7 a - 2\) , \( -4 a^{5} + 2 a^{4} + 26 a^{3} - 5 a^{2} - 38 a - 9\) , \( -23 a^{5} + 11 a^{4} + 155 a^{3} - 28 a^{2} - 237 a - 49\bigr] \)
29.1-a2	\( \bigl[a^{2} - 3\) , \( -2 a^{5} + a^{4} + 13 a^{3} - 2 a^{2} - 19 a - 5\) , \( -a^{5} + a^{4} + 6 a^{3} - 3 a^{2} - 7 a - 2\) , \( 1531 a^{5} - 743 a^{4} - 10369 a^{3} + 1820 a^{2} + 16027 a + 3286\) , \( 33441 a^{5} - 15713 a^{4} - 226728 a^{3} + 38407 a^{2} + 350175 a + 72382\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph