Elliptic curve isogeny class 27.3-c over number field 5.5.160801.1

• Base field: 5.5.160801.1
• Label: 5.5.160801.1-27.3-c
• Conductor: 27.3
• 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 27.3-c over 5.5.160801.1

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

Curve label	Weierstrass Coefficients
27.3-c1	\( \bigl[2 a^{4} - a^{3} - 9 a^{2} + 5 a + 3\) , \( 2 a^{4} - a^{3} - 10 a^{2} + 3 a + 3\) , \( 2 a^{4} - a^{3} - 10 a^{2} + 4 a + 5\) , \( 3 a^{4} - 7 a^{3} - 27 a^{2} + 24 a + 23\) , \( 4 a^{4} - 44 a^{3} - 92 a^{2} + 93 a + 90\bigr] \)
27.3-c2	\( \bigl[a^{2} + a - 1\) , \( a^{4} - 4 a^{2} - 1\) , \( a^{4} - 4 a^{2} + a + 1\) , \( 19 a^{4} - 30 a^{3} - 71 a^{2} + 120 a - 26\) , \( -88 a^{4} + 150 a^{3} + 340 a^{2} - 587 a + 131\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph