Elliptic curve isogeny class 29.2-b over number field \(\Q(\sqrt{5}, \sqrt{13})\)

• Base field: \(\Q(\sqrt{5}, \sqrt{13})\)
• Label: 4.4.4225.1-29.2-b
• Conductor: 29.2
• Rank: \( 0 \)

Base field \(\Q(\sqrt{5}, \sqrt{13})\)

Generator \(a\), with minimal polynomial \( x^{4} - 9 x^{2} + 4 \); class number \(1\).

Elliptic curves in class 29.2-b over \(\Q(\sqrt{5}, \sqrt{13})\)

Isogeny class 29.2-b contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
29.2-b1	\( \bigl[-\frac{1}{4} a^{3} + \frac{1}{2} a^{2} + \frac{9}{4} a - \frac{1}{2}\) , \( -\frac{1}{2} a^{2} + \frac{1}{2} a + 3\) , \( \frac{1}{4} a^{3} + \frac{1}{2} a^{2} - \frac{9}{4} a - \frac{5}{2}\) , \( -\frac{1}{2} a^{3} + \frac{11}{2} a\) , \( \frac{3}{4} a^{3} + \frac{1}{2} a^{2} - \frac{23}{4} a - \frac{7}{2}\bigr] \)
29.2-b2	\( \bigl[-\frac{1}{4} a^{3} + \frac{11}{4} a + \frac{1}{2}\) , \( -\frac{1}{2} a^{2} + \frac{3}{2} a + 2\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - 2\) , \( -a^{3} - \frac{1}{2} a^{2} + \frac{17}{2} a + 2\) , \( -\frac{1}{4} a^{3} - \frac{1}{2} a^{2} + \frac{5}{4} a + \frac{3}{2}\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph