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

Curve label	Weierstrass Coefficients
29.4-a1	\( \bigl[-\frac{4}{23} a^{3} + \frac{6}{23} a^{2} + \frac{63}{23} a - \frac{21}{23}\) , \( -\frac{1}{23} a^{3} - \frac{10}{23} a^{2} + \frac{33}{23} a + \frac{104}{23}\) , \( -\frac{1}{23} a^{3} + \frac{13}{23} a^{2} - \frac{13}{23} a - \frac{103}{23}\) , \( -\frac{9}{23} a^{3} + \frac{25}{23} a^{2} + \frac{228}{23} a + \frac{292}{23}\) , \( -\frac{83}{23} a^{3} - \frac{186}{23} a^{2} + \frac{554}{23} a + \frac{743}{23}\bigr] \)
29.4-a2	\( \bigl[-\frac{1}{23} a^{3} + \frac{13}{23} a^{2} - \frac{13}{23} a - \frac{103}{23}\) , \( \frac{4}{23} a^{3} - \frac{6}{23} a^{2} - \frac{63}{23} a + \frac{44}{23}\) , \( -\frac{1}{23} a^{3} + \frac{13}{23} a^{2} - \frac{13}{23} a - \frac{80}{23}\) , \( -\frac{42}{23} a^{3} + \frac{247}{23} a^{2} - \frac{201}{23} a - \frac{370}{23}\) , \( -\frac{250}{23} a^{3} + \frac{1295}{23} a^{2} - \frac{398}{23} a - \frac{2474}{23}\bigr] \)

Rank: \( 1 \)

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

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