Elliptic curve isogeny class 27.1-i over number field 6.6.1397493.1

• Base field: 6.6.1397493.1
• Label: 6.6.1397493.1-27.1-i
• Conductor: 27.1
• Rank: \( 1 \)

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-i over 6.6.1397493.1

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

Curve label	Weierstrass Coefficients
27.1-i1	\( \bigl[a^{4} - 2 a^{3} - 3 a^{2} + 4 a + 1\) , \( -a^{5} + 2 a^{4} + 7 a^{3} - 9 a^{2} - 13 a + 4\) , \( a^{3} - a^{2} - 2 a\) , \( 2 a^{5} - 6 a^{4} - 4 a^{3} + 14 a^{2} + 6 a - 2\) , \( a - 2\bigr] \)
27.1-i2	\( \bigl[a^{4} - 3 a^{3} + 6 a - 3\) , \( a^{5} - 2 a^{4} - 7 a^{3} + 10 a^{2} + 11 a - 5\) , \( a^{5} - 3 a^{4} - 2 a^{3} + 8 a^{2} + 2 a - 3\) , \( -2 a^{5} + 6 a^{4} + 8 a^{3} - 23 a^{2} - 11 a + 16\) , \( 5 a^{5} - 13 a^{4} - 18 a^{3} + 42 a^{2} + 24 a - 22\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph