Elliptic curve isogeny class 27.3-f over number field 5.5.160801.1

• Base field: 5.5.160801.1
• Label: 5.5.160801.1-27.3-f
• Conductor: 27.3
• Rank: \( 1 \)

Base field 5.5.160801.1

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

Elliptic curves in class 27.3-f over 5.5.160801.1

Isogeny class 27.3-f contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
27.3-f1	\( \bigl[2 a^{4} - a^{3} - 9 a^{2} + 5 a + 2\) , \( -a^{3} + a^{2} + 3 a - 2\) , \( a^{4} - 4 a^{2} + a + 1\) , \( -7 a^{4} + 10 a^{3} + 29 a^{2} - 43 a + 8\) , \( -a^{4} + a^{3} + 5 a^{2} - 6 a + 1\bigr] \)
27.3-f2	\( \bigl[a^{4} - 4 a^{2} + a + 1\) , \( -a^{4} + 4 a^{2} + a + 1\) , \( 2 a^{4} - a^{3} - 10 a^{2} + 4 a + 4\) , \( -2 a^{4} + 4 a^{3} + 16 a^{2} - 5 a - 9\) , \( 34 a^{4} - 19 a^{3} - 167 a^{2} + 81 a + 117\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph