Elliptic curve isogeny class 27.3-a over number field 5.5.160801.1

• Base field: 5.5.160801.1
• Label: 5.5.160801.1-27.3-a
• 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-a over 5.5.160801.1

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

Curve label	Weierstrass Coefficients
27.3-a1	\( \bigl[a^{4} - a^{3} - 5 a^{2} + 5 a + 2\) , \( -2 a^{4} + a^{3} + 9 a^{2} - 4 a - 1\) , \( 2 a^{4} - a^{3} - 10 a^{2} + 4 a + 5\) , \( 81 a^{4} - 64 a^{3} - 432 a^{2} + 218 a + 325\) , \( -809 a^{4} + 579 a^{3} + 4183 a^{2} - 2082 a - 2961\bigr] \)
27.3-a2	\( \bigl[2 a^{4} - a^{3} - 9 a^{2} + 5 a + 3\) , \( -a^{4} + a^{3} + 5 a^{2} - 4 a - 2\) , \( 2 a^{4} - a^{3} - 10 a^{2} + 5 a + 5\) , \( 6 a^{4} - 9 a^{3} - 12 a^{2} + 31 a - 18\) , \( 29 a^{4} - 39 a^{3} - 117 a^{2} + 189 a - 50\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph