LMFDB - Elliptic curve isogeny class 29.3-a over number field \(\Q(\sqrt{5}, \sqrt{7})\)

Base field \(\Q(\sqrt{5}, \sqrt{7})\)

Generator \(a\), with minimal polynomial \( x^{4} - 2 x^{3} - 15 x^{2} + 16 x + 29 \); class number \(1\).

Isogeny class 29.3-a contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
29.3-a1	\( \bigl[-\frac{3}{23} a^{3} + \frac{16}{23} a^{2} + \frac{30}{23} a - \frac{102}{23}\) , \( -a + 1\) , \( -\frac{3}{23} a^{3} + \frac{16}{23} a^{2} + \frac{30}{23} a - \frac{125}{23}\) , \( \frac{118}{23} a^{3} - \frac{361}{23} a^{2} - \frac{1433}{23} a + \frac{3414}{23}\) , \( \frac{594}{23} a^{3} - \frac{1811}{23} a^{2} - \frac{6998}{23} a + \frac{16677}{23}\bigr] \)
29.3-a2	\( \bigl[-\frac{4}{23} a^{3} + \frac{6}{23} a^{2} + \frac{63}{23} a - \frac{44}{23}\) , \( \frac{1}{23} a^{3} - \frac{13}{23} a^{2} - \frac{10}{23} a + \frac{126}{23}\) , \( -\frac{2}{23} a^{3} + \frac{3}{23} a^{2} + \frac{43}{23} a + \frac{1}{23}\) , \( -\frac{13}{23} a^{3} - \frac{61}{23} a^{2} + \frac{245}{23} a + \frac{961}{23}\) , \( \frac{162}{23} a^{3} - \frac{59}{23} a^{2} - \frac{2333}{23} a - \frac{1369}{23}\bigr] \)

Rank: \( 1 \)

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi