Properties

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

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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-a over \(\Q(\sqrt{5}, \sqrt{13})\)

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

Curve label Weierstrass Coefficients
29.2-a1 \( \bigl[\frac{1}{4} a^{3} + \frac{1}{2} a^{2} - \frac{9}{4} a - \frac{5}{2}\) , \( -\frac{1}{4} a^{3} + \frac{1}{2} a^{2} + \frac{9}{4} a - \frac{3}{2}\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - 1\) , \( -\frac{1}{4} a^{3} - \frac{3}{2} a^{2} + \frac{5}{4} a + \frac{7}{2}\) , \( -\frac{25}{4} a^{3} + 3 a^{2} + \frac{203}{4} a - \frac{65}{2}\bigr] \)
29.2-a2 \( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 2\) , \( -\frac{1}{2} a^{3} - \frac{1}{2} a^{2} + 5 a + 4\) , \( \frac{1}{4} a^{3} + \frac{1}{2} a^{2} - \frac{9}{4} a - \frac{5}{2}\) , \( \frac{1}{4} a^{3} + \frac{1}{2} a^{2} - \frac{5}{4} a - \frac{11}{2}\) , \( -57 a^{3} - \frac{77}{2} a^{2} + \frac{973}{2} a + 328\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph