Elliptic curve isogeny class 27.1-a over number field 5.5.160801.1

• Base field: 5.5.160801.1
• Label: 5.5.160801.1-27.1-a
• Conductor: 27.1
• 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 27.1-a over 5.5.160801.1

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

Curve label	Weierstrass Coefficients
27.1-a1	\( \bigl[a^{2} - 2\) , \( a^{4} - a^{3} - 6 a^{2} + 5 a + 3\) , \( 2 a^{4} - a^{3} - 10 a^{2} + 4 a + 4\) , \( 4 a^{4} - 3 a^{3} - 21 a^{2} + 13 a + 10\) , \( -2 a^{3} + 11 a^{2} - 16 a + 3\bigr] \)
27.1-a2	\( \bigl[a^{4} - 5 a^{2} + 3\) , \( a^{3} - a^{2} - 3 a + 2\) , \( a^{4} - a^{3} - 4 a^{2} + 4 a + 1\) , \( -24 a^{4} - 9 a^{3} + 115 a^{2} + 58 a - 24\) , \( 2670 a^{4} + 599 a^{3} - 12619 a^{2} - 4772 a + 2184\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph