Elliptic curve isogeny class 27.1-p over number field 6.6.1387029.1

• Base field: 6.6.1387029.1
• Label: 6.6.1387029.1-27.1-p
• Conductor: 27.1
• Rank: \( 0 \)

Base field 6.6.1387029.1

Generator \(a\), with minimal polynomial \( x^{6} - 3 x^{5} - 2 x^{4} + 9 x^{3} - x^{2} - 4 x + 1 \); class number \(1\).

Elliptic curves in class 27.1-p over 6.6.1387029.1

Isogeny class 27.1-p contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
27.1-p1	\( \bigl[-a^{5} + 3 a^{4} + 3 a^{3} - 8 a^{2} - 4 a + 2\) , \( a^{5} - 3 a^{4} - a^{3} + 8 a^{2} - 5 a - 2\) , \( -a^{5} + 3 a^{4} + 3 a^{3} - 9 a^{2} - 2 a + 3\) , \( -3 a^{5} + 10 a^{3} + 5 a^{2} - 10 a - 2\) , \( a^{5} + 4 a^{4} - 6 a^{3} - 8 a^{2} + 4 a - 3\bigr] \)
27.1-p2	\( \bigl[a^{3} - 4 a + 1\) , \( 3 a^{5} - 7 a^{4} - 9 a^{3} + 18 a^{2} + 4 a - 5\) , \( -a^{5} + 3 a^{4} + 2 a^{3} - 7 a^{2} + 2\) , \( 7 a^{5} - 34 a^{4} + 40 a^{3} + 16 a^{2} - 31 a + 10\) , \( 53 a^{5} - 232 a^{4} + 239 a^{3} + 81 a^{2} - 149 a + 29\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph