Elliptic curve isogeny class 27.2-a over number field 5.5.160801.1

• Base field: 5.5.160801.1
• Label: 5.5.160801.1-27.2-a
• Conductor: 27.2
• Rank: \( 0 \)

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 27.2-a over 5.5.160801.1

Isogeny class 27.2-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
27.2-a1	\( \bigl[a^{4} - 4 a^{2} + 1\) , \( a^{4} - 6 a^{2} + a + 3\) , \( a^{4} - a^{3} - 5 a^{2} + 5 a + 2\) , \( 22 a^{4} - 5 a^{3} - 99 a^{2} + 7 a + 7\) , \( 71 a^{4} - 12 a^{3} - 314 a^{2} - 21 a + 27\bigr] \)
27.2-a2	\( \bigl[a^{4} - 5 a^{2} + 3\) , \( a^{4} - a^{3} - 4 a^{2} + 4 a\) , \( 2 a^{4} - a^{3} - 9 a^{2} + 5 a + 2\) , \( 2 a^{4} - a^{3} - 10 a^{2} + 3 a + 3\) , \( a^{4} - 2 a^{3} - 4 a^{2} + 7 a - 5\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph