Properties

Base field \(\Q(\sqrt{5}, \sqrt{13})\)
Label 4.4.4225.1-29.3-a
Conductor 29.3
Rank \( 0 \)

Related objects

Learn more

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

Isogeny class 29.3-a contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
29.3-a1 \( \bigl[\frac{1}{2} a^{2} - \frac{1}{2} a - 2\) , \( -\frac{1}{4} a^{3} + \frac{7}{4} a + \frac{1}{2}\) , \( \frac{1}{2} a^{2} - \frac{1}{2} a - 1\) , \( -\frac{3}{2} a^{3} - 4 a^{2} + \frac{5}{2} a + 2\) , \( \frac{9}{2} a^{3} + 12 a^{2} - \frac{9}{2} a - 7\bigr] \)
29.3-a2 \( \bigl[\frac{1}{2} a^{2} + \frac{1}{2} a - 2\) , \( -\frac{1}{4} a^{3} - \frac{1}{2} a^{2} + \frac{13}{4} a + \frac{5}{2}\) , \( \frac{1}{2} a^{2} + \frac{1}{2} a - 2\) , \( -\frac{11}{4} a^{3} + 2 a^{2} + \frac{89}{4} a - \frac{25}{2}\) , \( \frac{243}{4} a^{3} - 41 a^{2} - \frac{2069}{4} a + \frac{695}{2}\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph