Elliptic curve isogeny class 16.1-c over number field 5.5.81509.1

• Base field: 5.5.81509.1
• Label: 5.5.81509.1-16.1-c
• Conductor: 16.1
• Rank: \( 0 \)

Base field 5.5.81509.1

Generator \(a\), with minimal polynomial \( x^{5} - x^{4} - 5 x^{3} + 3 x^{2} + 5 x - 2 \); class number \(1\).

Elliptic curves in class 16.1-c over 5.5.81509.1

Isogeny class 16.1-c contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
16.1-c1	\( \bigl[a^{4} - a^{3} - 4 a^{2} + 3 a + 3\) , \( a^{2} - a - 1\) , \( a^{2} - 2\) , \( 41 a^{4} + 16 a^{3} - 205 a^{2} - 129 a + 76\) , \( 254 a^{4} + 87 a^{3} - 1250 a^{2} - 773 a + 445\bigr] \)
16.1-c2	\( \bigl[a + 1\) , \( -a^{4} + 4 a^{2} + 2 a - 1\) , \( a^{4} - 5 a^{2} + 4\) , \( a^{3} - a^{2} - 5 a - 3\) , \( 12 a^{4} + 4 a^{3} - 57 a^{2} - 40 a + 14\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph