Elliptic curve isogeny class 27.1-j over number field 6.6.1397493.1

• Base field: 6.6.1397493.1
• Label: 6.6.1397493.1-27.1-j
• Conductor: 27.1
• Rank: \( 0 \)

Base field 6.6.1397493.1

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

Elliptic curves in class 27.1-j over 6.6.1397493.1

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

Curve label	Weierstrass Coefficients
27.1-j1	\( \bigl[a^{3} - a^{2} - 3 a\) , \( -a^{5} + 3 a^{4} + 3 a^{3} - 9 a^{2} - 4 a + 2\) , \( a^{5} - 2 a^{4} - 5 a^{3} + 6 a^{2} + 8 a - 1\) , \( -3 a^{4} + a^{3} + 11 a^{2} + 4 a - 1\) , \( -5 a^{5} + 4 a^{4} + 19 a^{3} - 8 a^{2} - 16 a + 3\bigr] \)
27.1-j2	\( \bigl[a^{5} - 2 a^{4} - 5 a^{3} + 7 a^{2} + 8 a - 3\) , \( -a^{3} + 2 a^{2} + 2 a - 3\) , \( a^{5} - 2 a^{4} - 5 a^{3} + 7 a^{2} + 8 a - 3\) , \( 7 a^{5} - 2 a^{4} - 36 a^{3} - 24 a^{2} + 6 a + 1\) , \( -59 a^{5} + 55 a^{4} + 293 a^{3} + 16 a^{2} - 155 a + 27\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph