Elliptic curve isogeny class 16.2-b over number field 4.4.16609.1

• Base field: 4.4.16609.1
• Label: 4.4.16609.1-16.2-b
• Conductor: 16.2
• Rank: \( 0 \)

Base field 4.4.16609.1

Generator \(a\), with minimal polynomial \( x^{4} - 7 x^{2} - x + 9 \); class number \(1\).

Elliptic curves in class 16.2-b over 4.4.16609.1

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

Curve label	Weierstrass Coefficients
16.2-b1	\( \bigl[a^{2} + a - 4\) , \( 0\) , \( a^{3} - 3 a\) , \( -25 a^{3} + 35 a^{2} + 122 a - 153\) , \( 61 a^{3} - 92 a^{2} - 293 a + 373\bigr] \)
16.2-b2	\( \bigl[a^{3} - a^{2} - 3 a + 3\) , \( -a^{3} + 4 a + 1\) , \( a^{3} - 4 a - 1\) , \( -3 a^{3} - 4 a^{2} + 12 a + 30\) , \( -a^{3} - 2 a^{2} + 2 a + 18\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph