Elliptic curve isogeny class 27.1-b over number field 6.6.434581.1

• Base field: 6.6.434581.1
• Label: 6.6.434581.1-27.1-b
• Conductor: 27.1
• 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 27.1-b over 6.6.434581.1

Isogeny class 27.1-b contains only one elliptic curve.

Curve label	Weierstrass Coefficients
27.1-b1	\( \bigl[a^{4} - 2 a^{3} - 3 a^{2} + 4 a + 1\) , \( -2 a^{5} + 5 a^{4} + 5 a^{3} - 12 a^{2} + a + 4\) , \( a^{5} - 2 a^{4} - 4 a^{3} + 5 a^{2} + 3 a - 1\) , \( -2 a^{5} + 4 a^{4} + 7 a^{3} - 9 a^{2} - 5 a + 5\) , \( -18 a^{5} + 41 a^{4} + 60 a^{3} - 112 a^{2} - 32 a + 48\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph