Elliptic curve isogeny class 27.2-a over number field 6.6.434581.1

• Base field: 6.6.434581.1
• Label: 6.6.434581.1-27.2-a
• Conductor: 27.2
• Rank: \( 0 \)

Base field 6.6.434581.1

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

Elliptic curves in class 27.2-a over 6.6.434581.1

Isogeny class 27.2-a contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
27.2-a1	\( \bigl[a + 1\) , \( a^{5} - 4 a^{4} + 12 a^{2} - 3 a - 4\) , \( a^{5} - 2 a^{4} - 4 a^{3} + 5 a^{2} + 4 a - 1\) , \( -2 a^{5} + 3 a^{4} + 8 a^{3} - 6 a - 1\) , \( -3 a^{5} + 6 a^{4} + 10 a^{3} - 10 a^{2} - 3 a\bigr] \)
27.2-a2	\( \bigl[2 a^{5} - 4 a^{4} - 7 a^{3} + 8 a^{2} + 5 a - 2\) , \( -a^{2} + a\) , \( 2 a^{5} - 5 a^{4} - 5 a^{3} + 12 a^{2} - 3\) , \( -10 a^{5} + 23 a^{4} + 29 a^{3} - 48 a^{2} - 13 a + 2\) , \( -18 a^{5} + 38 a^{4} + 59 a^{3} - 78 a^{2} - 35 a\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph