Elliptic curve isogeny class 27.1-f over number field 6.6.1397493.1

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

Isogeny class 27.1-f contains only one elliptic curve.

Curve label	Weierstrass Coefficients
27.1-f1	\( \bigl[a^{4} - 2 a^{3} - 3 a^{2} + 5 a + 2\) , \( a^{5} - 3 a^{4} - 3 a^{3} + 10 a^{2} + 2 a - 4\) , \( a^{5} - 2 a^{4} - 5 a^{3} + 7 a^{2} + 8 a - 4\) , \( -8 a^{5} + 26 a^{4} + 29 a^{3} - 87 a^{2} - 67 a + 20\) , \( 26 a^{5} - 47 a^{4} - 122 a^{3} + 117 a^{2} + 147 a - 34\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph