Elliptic curve isogeny class 27.1-b over number field 6.6.1397493.1

• Base field: 6.6.1397493.1
• Label: 6.6.1397493.1-27.1-b
• Conductor: 27.1
• Rank: \( 1 \)

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-b over 6.6.1397493.1

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

Curve label	Weierstrass Coefficients
27.1-b1	\( \bigl[a^{5} - 3 a^{4} - 3 a^{3} + 9 a^{2} + 4 a - 3\) , \( a^{4} - 2 a^{3} - 4 a^{2} + 4 a + 3\) , \( a^{5} - 3 a^{4} - 2 a^{3} + 7 a^{2} + 2 a\) , \( -2 a^{5} + 5 a^{4} + 7 a^{3} - 15 a^{2} - 6 a + 9\) , \( -a^{5} + 4 a^{4} + a^{3} - 12 a^{2} - 2 a + 4\bigr] \)
27.1-b2	\( \bigl[a^{5} - 3 a^{4} - 3 a^{3} + 9 a^{2} + 4 a - 2\) , \( a^{5} - 2 a^{4} - 5 a^{3} + 5 a^{2} + 8 a - 1\) , \( a^{2} - 1\) , \( 6 a^{5} - 13 a^{4} - 32 a^{3} + 45 a^{2} + 58 a - 13\) , \( 9 a^{5} - 20 a^{4} - 46 a^{3} + 65 a^{2} + 79 a - 18\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph