Elliptic curve isogeny class 27.1-k over number field 6.6.1397493.1

• Base field: 6.6.1397493.1
• Label: 6.6.1397493.1-27.1-k
• 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-k over 6.6.1397493.1

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

Curve label	Weierstrass Coefficients
27.1-k1	\( \bigl[a^{3} - 2 a^{2} - 2 a + 3\) , \( -a^{5} + 2 a^{4} + 5 a^{3} - 5 a^{2} - 8 a + 1\) , \( a^{4} - 2 a^{3} - 2 a^{2} + 4 a - 1\) , \( 2 a^{5} - 3 a^{4} - 5 a^{3} + 7 a^{2} + 3 a - 1\) , \( -3 a^{5} + 3 a^{4} + 10 a^{3} - 4 a^{2} - 4 a + 1\bigr] \)
27.1-k2	\( \bigl[a^{3} - 2 a^{2} - 2 a + 2\) , \( -a^{5} + 2 a^{4} + 7 a^{3} - 9 a^{2} - 12 a + 3\) , \( a^{5} - 3 a^{4} - 2 a^{3} + 8 a^{2} + 2 a - 2\) , \( 4 a^{5} - 9 a^{4} - 20 a^{3} + 30 a^{2} + 34 a - 7\) , \( -5 a^{5} + 12 a^{4} + 22 a^{3} - 37 a^{2} - 36 a + 8\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph