Elliptic curve isogeny class 27.1-d over number field 6.6.1387029.1

• Base field: 6.6.1387029.1
• Label: 6.6.1387029.1-27.1-d
• Conductor: 27.1
• Rank: \( 0 \)

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-d over 6.6.1387029.1

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

Curve label	Weierstrass Coefficients
27.1-d1	\( \bigl[a^{2} - a - 1\) , \( a^{2} - a\) , \( a^{2}\) , \( 5 a^{5} - 13 a^{4} - 15 a^{3} + 41 a^{2} + 6 a - 19\) , \( -8 a^{5} + 22 a^{4} + 21 a^{3} - 65 a^{2} - 10 a + 28\bigr] \)
27.1-d2	\( \bigl[-2 a^{5} + 5 a^{4} + 6 a^{3} - 13 a^{2} - 4 a + 4\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 3 a + 2\) , \( a^{4} - a^{3} - 3 a^{2} + 1\) , \( -6 a^{5} + 17 a^{4} + 8 a^{3} - 29 a^{2} - 8 a + 6\) , \( -2 a^{5} - 13 a^{4} + 76 a^{3} - 55 a^{2} - 61 a + 19\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph