Elliptic curve isogeny class 16.2-b over number field 5.5.138136.1

• Base field: 5.5.138136.1
• Label: 5.5.138136.1-16.2-b
• Conductor: 16.2
• 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 16.2-b over 5.5.138136.1

Isogeny class 16.2-b contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
16.2-b1	\( \bigl[a^{4} - 7 a^{2} - a + 6\) , \( -a^{3} + a^{2} + 5 a - 1\) , \( 2 a^{4} - a^{3} - 12 a^{2} + 6\) , \( a^{4} - 3 a^{3} - 3 a^{2} + 11 a - 1\) , \( 4 a^{4} - 6 a^{3} - 18 a^{2} + 20 a - 2\bigr] \)
16.2-b2	\( \bigl[a^{4} - 7 a^{2} - 2 a + 6\) , \( -a^{2} + a + 4\) , \( 2 a^{4} - a^{3} - 12 a^{2} + 6\) , \( 8 a^{4} - 3 a^{3} - 53 a^{2} - 4 a + 40\) , \( -14 a^{4} + 6 a^{3} + 89 a^{2} + 4 a - 54\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph