Elliptic curve isogeny class 27.3-e over number field 5.5.160801.1

• Base field: 5.5.160801.1
• Label: 5.5.160801.1-27.3-e
• Conductor: 27.3
• Rank: \( 2 \)

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-e over 5.5.160801.1

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

Curve label	Weierstrass Coefficients
27.3-e1	\( \bigl[a^{2} - 2\) , \( -a^{4} + a^{3} + 4 a^{2} - 3 a\) , \( a^{2} + a - 1\) , \( -2 a^{4} + 2 a^{3} + 6 a^{2} - 5 a\) , \( -2 a^{3} + 3 a^{2} - a\bigr] \)
27.3-e2	\( \bigl[a^{4} - a^{3} - 4 a^{2} + 4 a + 1\) , \( a^{4} - 6 a^{2} + a + 5\) , \( a^{4} - a^{3} - 5 a^{2} + 4 a + 3\) , \( a^{4} - 4 a^{2} - a + 4\) , \( -2 a^{4} + 2 a^{3} + 10 a^{2} - 6 a - 6\bigr] \)

Rank

Rank: \( 2 \)

Isogeny matrix

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

Isogeny graph