Elliptic curve isogeny class 27.1-b over number field 5.5.36497.1

• Base field: 5.5.36497.1
• Label: 5.5.36497.1-27.1-b
• Conductor: 27.1
• Rank: \( 1 \)

Base field 5.5.36497.1

Generator \(a\), with minimal polynomial \( x^{5} - 2 x^{4} - 3 x^{3} + 5 x^{2} + x - 1 \); class number \(1\).

Elliptic curves in class 27.1-b over 5.5.36497.1

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

Curve label	Weierstrass Coefficients
27.1-b1	\( \bigl[2 a^{4} - 3 a^{3} - 6 a^{2} + 6 a + 1\) , \( -a^{4} + a^{3} + 3 a^{2} - a + 1\) , \( 2 a^{4} - 3 a^{3} - 6 a^{2} + 7 a + 2\) , \( -5 a^{4} + 6 a^{3} + 16 a^{2} - 9 a - 5\) , \( -3 a^{4} + 3 a^{3} + 10 a^{2} - 5 a - 3\bigr] \)
27.1-b2	\( \bigl[2 a^{4} - 3 a^{3} - 7 a^{2} + 8 a + 3\) , \( a^{3} - 5 a - 2\) , \( a^{4} - a^{3} - 3 a^{2} + a\) , \( -5 a^{3} + 2 a^{2} + 16 a - 1\) , \( 4 a^{4} - 4 a^{3} - 16 a^{2} + 6 a + 10\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph