Elliptic curve isogeny class 16.2-a over number field \(\Q(\sqrt{5}, \sqrt{21})\)

• Base field: \(\Q(\sqrt{5}, \sqrt{21})\)
• Label: 4.4.11025.1-16.2-a
• Conductor: 16.2
• Rank: \( 0 \)

Base field \(\Q(\sqrt{5}, \sqrt{21})\)

Generator \(a\), with minimal polynomial \( x^{4} - 13 x^{2} + 16 \); class number \(1\).

Elliptic curves in class 16.2-a over \(\Q(\sqrt{5}, \sqrt{21})\)

Isogeny class 16.2-a contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
16.2-a1	\( \bigl[0\) , \( \frac{1}{8} a^{3} - \frac{17}{8} a - \frac{3}{2}\) , \( a\) , \( -\frac{1}{8} a^{3} + \frac{17}{8} a + \frac{5}{2}\) , \( 7 a^{3} - \frac{47}{2} a^{2} - \frac{21}{2} a + 31\bigr] \)
16.2-a2	\( \bigl[0\) , \( -\frac{1}{8} a^{3} + \frac{17}{8} a + \frac{3}{2}\) , \( a\) , \( -\frac{1}{8} a^{3} + \frac{17}{8} a + \frac{5}{2}\) , \( -7 a^{3} - \frac{47}{2} a^{2} + \frac{21}{2} a + 33\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph