Elliptic curve isogeny class 27.1-e over number field 6.6.1387029.1

• Base field: 6.6.1387029.1
• Label: 6.6.1387029.1-27.1-e
• Conductor: 27.1
• Rank: \( 1 \)

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-e over 6.6.1387029.1

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

Curve label	Weierstrass Coefficients
27.1-e1	\( \bigl[-2 a^{5} + 5 a^{4} + 6 a^{3} - 13 a^{2} - 4 a + 3\) , \( 2 a^{5} - 4 a^{4} - 8 a^{3} + 11 a^{2} + 6 a - 2\) , \( -a^{5} + 3 a^{4} + 2 a^{3} - 8 a^{2} + 2\) , \( 9 a^{5} - 20 a^{4} - 34 a^{3} + 60 a^{2} + 30 a - 21\) , \( 6 a^{5} - 17 a^{4} - 18 a^{3} + 57 a^{2} + 17 a - 20\bigr] \)
27.1-e2	\( \bigl[-a^{5} + 3 a^{4} + 3 a^{3} - 9 a^{2} - 3 a + 4\) , \( -2 a^{5} + 5 a^{4} + 5 a^{3} - 12 a^{2} - a + 2\) , \( -a^{5} + 3 a^{4} + 3 a^{3} - 9 a^{2} - 3 a + 3\) , \( 10 a^{5} - 27 a^{4} - 25 a^{3} + 80 a^{2} + 8 a - 34\) , \( 29 a^{5} - 77 a^{4} - 78 a^{3} + 229 a^{2} + 36 a - 102\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph