Elliptic curve isogeny class 16.1-b over number field 4.4.9909.1

• Base field: 4.4.9909.1
• Label: 4.4.9909.1-16.1-b
• 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-b over 4.4.9909.1

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

Curve label	Weierstrass Coefficients
16.1-b1	\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( 16 a^{3} + 8 a^{2} - 86 a - 106\) , \( 12 a^{3} + 2 a^{2} - 55 a - 81\bigr] \)
16.1-b2	\( \bigl[a^{3} - a^{2} - 4 a + 2\) , \( a^{2} - 4\) , \( a^{2} - a - 2\) , \( -17 a^{3} + 20 a^{2} + 78 a - 38\) , \( -523 a^{3} + 632 a^{2} + 2376 a - 1303\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph