Elliptic curve isogeny class 27.1-o over number field 6.6.1397493.1

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

Isogeny class 27.1-o contains only one elliptic curve.

Curve label	Weierstrass Coefficients
27.1-o1	\( \bigl[a^{2} - 2\) , \( a^{5} - 3 a^{4} - 2 a^{3} + 8 a^{2} + a - 3\) , \( a^{2} - 2\) , \( -3 a^{4} + 13 a^{3} - 4 a^{2} - 23 a + 3\) , \( -5 a^{5} + 18 a^{4} + a^{3} - 33 a^{2} - 4 a + 1\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph