LMFDB - Elliptic curve isogeny class 29.4-b 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 29.4-b contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
29.4-b1	\( \bigl[\frac{1}{23} a^{3} + \frac{10}{23} a^{2} - \frac{33}{23} a - \frac{58}{23}\) , \( -\frac{1}{23} a^{3} + \frac{13}{23} a^{2} - \frac{13}{23} a - \frac{126}{23}\) , \( \frac{1}{23} a^{3} + \frac{10}{23} a^{2} - \frac{33}{23} a - \frac{58}{23}\) , \( \frac{14}{23} a^{3} + \frac{48}{23} a^{2} - \frac{209}{23} a - \frac{122}{23}\) , \( \frac{70}{23} a^{3} + \frac{240}{23} a^{2} - \frac{470}{23} a - \frac{725}{23}\bigr] \)
29.4-b2	\( \bigl[-\frac{3}{23} a^{3} + \frac{16}{23} a^{2} + \frac{30}{23} a - \frac{102}{23}\) , \( -a\) , \( 1\) , \( -\frac{43}{23} a^{3} + \frac{237}{23} a^{2} - \frac{191}{23} a - \frac{197}{23}\) , \( \frac{24}{23} a^{3} - \frac{105}{23} a^{2} - \frac{79}{23} a + \frac{379}{23}\bigr] \)

Rank: \( 1 \)

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

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