Elliptic curve isogeny class 16.1-b over number field 4.4.11525.1

• Base field: 4.4.11525.1
• Label: 4.4.11525.1-16.1-b
• Conductor: 16.1
• Rank: \( 1 \)

Base field 4.4.11525.1

Generator \(a\), with minimal polynomial \( x^{4} - x^{3} - 11 x^{2} + 5 x + 25 \); class number \(1\).

Elliptic curves in class 16.1-b over 4.4.11525.1

Isogeny class 16.1-b contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
16.1-b1	\( \bigl[1\) , \( \frac{1}{5} a^{3} - \frac{6}{5} a^{2} - \frac{6}{5} a + 5\) , \( \frac{1}{5} a^{3} - \frac{1}{5} a^{2} - \frac{1}{5} a\) , \( -\frac{398}{5} a^{3} + \frac{948}{5} a^{2} + \frac{3188}{5} a - 1377\) , \( -\frac{7413}{5} a^{3} + \frac{18473}{5} a^{2} + \frac{54578}{5} a - 24329\bigr] \)
16.1-b2	\( \bigl[1\) , \( \frac{1}{5} a^{3} - \frac{6}{5} a^{2} - \frac{6}{5} a + 5\) , \( \frac{1}{5} a^{3} - \frac{1}{5} a^{2} - \frac{1}{5} a\) , \( \frac{2}{5} a^{3} - \frac{2}{5} a^{2} - \frac{12}{5} a + 3\) , \( -\frac{29}{5} a^{3} + \frac{69}{5} a^{2} + \frac{204}{5} a - 89\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph