Elliptic curve isogeny class 29.3-c over number field 6.6.1279733.1

• Base field: 6.6.1279733.1
• Label: 6.6.1279733.1-29.3-c
• Conductor: 29.3
• Rank: \( 0 \)

Base field 6.6.1279733.1

Generator \(a\), with minimal polynomial \( x^{6} - 2 x^{5} - 6 x^{4} + 10 x^{3} + 10 x^{2} - 11 x - 1 \); class number \(1\).

Elliptic curves in class 29.3-c over 6.6.1279733.1

Isogeny class 29.3-c contains 2 curves linked by isogenies of degree 5.

Curve label	Weierstrass Coefficients
29.3-c1	\( \bigl[a^{2} - 2\) , \( a^{5} - 2 a^{4} - 4 a^{3} + 6 a^{2} + 5 a - 2\) , \( a^{5} - 2 a^{4} - 2 a^{3} + 6 a^{2} - 3 a - 2\) , \( 65 a^{5} - 151 a^{4} - 347 a^{3} + 706 a^{2} + 535 a - 744\) , \( 8693 a^{5} - 18199 a^{4} - 50436 a^{3} + 91318 a^{2} + 78787 a - 102152\bigr] \)
29.3-c2	\( \bigl[a + 1\) , \( a^{5} - a^{4} - 5 a^{3} + 3 a^{2} + 6 a\) , \( a^{3} - 3 a\) , \( 2 a^{5} - a^{4} - 11 a^{3} + 2 a^{2} + 14 a + 1\) , \( 0\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph