Elliptic curve isogeny class 16.1-b over number field 4.4.13824.1

• Base field: 4.4.13824.1
• Label: 4.4.13824.1-16.1-b
• Conductor: 16.1
• Rank: \( 1 \)

Base field 4.4.13824.1

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

Elliptic curves in class 16.1-b over 4.4.13824.1

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

Curve label	Weierstrass Coefficients
16.1-b1	\( \bigl[a^{3} - 4 a\) , \( -a^{3} + 4 a + 1\) , \( a^{2} - 2\) , \( -4 a^{2} - 2 a + 20\) , \( 5 a^{3} - 9 a^{2} - 24 a + 41\bigr] \)
16.1-b2	\( \bigl[a^{3} + a^{2} - 4 a - 2\) , \( -a^{3} - a^{2} + 5 a + 3\) , \( a^{3} + a^{2} - 3 a - 2\) , \( a^{3} + a^{2} - 8 a - 10\) , \( -a^{3} - 2 a^{2} + 2 a + 3\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph