Elliptic curve isogeny class 16.1-c over number field 4.4.18688.1

• Base field: 4.4.18688.1
• Label: 4.4.18688.1-16.1-c
• Conductor: 16.1
• Rank: \( 0 \)

Base field 4.4.18688.1

Generator \(a\), with minimal polynomial \( x^{4} - 10 x^{2} - 4 x + 14 \); class number \(1\).

Elliptic curves in class 16.1-c over 4.4.18688.1

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

Curve label	Weierstrass Coefficients
16.1-c1	\( \bigl[0\) , \( -\frac{2}{3} a^{3} + \frac{5}{3} a^{2} + 3 a - \frac{22}{3}\) , \( -\frac{1}{3} a^{3} + \frac{4}{3} a^{2} + 2 a - \frac{14}{3}\) , \( a^{2} + 2\) , \( -\frac{2}{3} a^{3} - \frac{1}{3} a^{2} + 2 a - \frac{7}{3}\bigr] \)
16.1-c2	\( \bigl[0\) , \( \frac{2}{3} a^{3} - \frac{5}{3} a^{2} - 3 a + \frac{16}{3}\) , \( -\frac{1}{3} a^{3} + \frac{4}{3} a^{2} + 2 a - \frac{14}{3}\) , \( a^{2} - 4 a + 2\) , \( a^{3} - 3 a^{2} - 4 a + 6\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph