Elliptic curve isogeny class 27.1-n over number field 6.6.1387029.1

• Base field: 6.6.1387029.1
• Label: 6.6.1387029.1-27.1-n
• Conductor: 27.1
• Rank: \( 1 \)

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-n over 6.6.1387029.1

Isogeny class 27.1-n contains only one elliptic curve.

Curve label	Weierstrass Coefficients
27.1-n1	\( \bigl[-a^{5} + 2 a^{4} + 5 a^{3} - 6 a^{2} - 6 a + 3\) , \( -a^{3} + 2 a^{2} + 3 a - 1\) , \( a^{4} - 2 a^{3} - 2 a^{2} + 4 a\) , \( -2 a^{5} + 8 a^{4} + 9 a^{3} - 20 a^{2} - 9 a + 7\) , \( 4 a^{5} + 4 a^{4} - 12 a^{3} - 10 a^{2} + 6 a + 1\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{r} 1 \end{array}\right)\)

Isogeny graph