Elliptic curve isogeny class 16.1-b over number field 5.5.138136.1

• Base field: 5.5.138136.1
• Label: 5.5.138136.1-16.1-b
• Conductor: 16.1
• Rank: \( 1 \)

Base field 5.5.138136.1

Generator \(a\), with minimal polynomial \( x^{5} - x^{4} - 6 x^{3} + 3 x^{2} + 4 x - 2 \); class number \(1\).

Elliptic curves in class 16.1-b over 5.5.138136.1

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

Curve label	Weierstrass Coefficients
16.1-b1	\( \bigl[a^{4} - 6 a^{2} - 2 a + 3\) , \( -a^{4} + 7 a^{2} + 3 a - 5\) , \( a^{4} - 6 a^{2} - 2 a + 2\) , \( a^{4} + a^{3} - 6 a^{2} - 5 a + 5\) , \( a^{4} + a^{3} - 5 a^{2} - 4 a + 3\bigr] \)
16.1-b2	\( \bigl[1\) , \( -2 a^{4} + a^{3} + 12 a^{2} - 7\) , \( 4 a^{4} - a^{3} - 25 a^{2} - 5 a + 14\) , \( -75 a^{4} + 36 a^{3} + 469 a^{2} + 18 a - 291\) , \( 443 a^{4} - 215 a^{3} - 2769 a^{2} - 97 a + 1721\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph