Elliptic curve isogeny class 16.1-a over number field 4.4.9909.1

• Base field: 4.4.9909.1
• Label: 4.4.9909.1-16.1-a
• Conductor: 16.1
• Rank: \( 1 \)

Base field 4.4.9909.1

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

Elliptic curves in class 16.1-a over 4.4.9909.1

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

Curve label	Weierstrass Coefficients
16.1-a1	\( \bigl[a^{2} - 3\) , \( a^{2} - a - 3\) , \( a^{2} - 3\) , \( 104 a^{3} + 58 a^{2} - 602 a - 641\) , \( -354 a^{3} - 185 a^{2} + 2035 a + 2117\bigr] \)
16.1-a2	\( \bigl[a^{2} - 2\) , \( -a^{3} + 2 a^{2} + 2 a - 4\) , \( a^{2} - a - 2\) , \( 2 a^{3} - 4 a^{2} - 6 a + 3\) , \( -a - 1\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph