Elliptic curve isogeny class 16.1-b over number field 4.4.12357.1

• Base field: 4.4.12357.1
• Label: 4.4.12357.1-16.1-b
• Number of curves: 3
• Conductor: 16.1
• Rank bounds: 0...1

Base field 4.4.12357.1

Generator \(a\), with minimal polynomial \( x^{4} - x^{3} - 5 x^{2} + 3 x + 3 \); class number \(1\).

Rank

Rank \(r\) satisfies \(0 \le r \le 1\)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)

Isogeny graph

Elliptic curves in class 16.1-b over 4.4.12357.1

Isogeny class 16.1-b contains 3 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
16.1-b1	\( \bigl[a^{2} - 3\) , \( a^{3} - 4 a - 2\) , \( a^{2} + a - 3\) , \( -81 a^{3} + 102 a^{2} + 343 a - 318\) , \( -257 a^{3} - 912 a^{2} + 1591 a + 4663\bigr] \)
16.1-b2	\( \bigl[a^{2} + a - 3\) , \( a^{2} - 2\) , \( 0\) , \( 2 a^{3} + 4 a^{2} - 6 a - 4\) , \( 4 a^{3} - 2 a^{2} - 4 a\bigr] \)
16.1-b3	\( \bigl[a^{3} - a^{2} - 3 a + 3\) , \( a^{3} - 2 a^{2} - 3 a + 4\) , \( a\) , \( -a^{3} + a^{2} + 3 a - 3\) , \( -a^{2} + 1\bigr] \)