LMFDB - Elliptic curve isogeny class 29.2-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 29.2-a contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
29.2-a1	\( \bigl[-\frac{1}{23} a^{3} + \frac{13}{23} a^{2} - \frac{13}{23} a - \frac{103}{23}\) , \( \frac{4}{23} a^{3} - \frac{6}{23} a^{2} - \frac{63}{23} a + \frac{44}{23}\) , \( -\frac{2}{23} a^{3} + \frac{3}{23} a^{2} + \frac{43}{23} a - \frac{22}{23}\) , \( -\frac{121}{23} a^{3} + \frac{9}{23} a^{2} + \frac{1693}{23} a + \frac{1866}{23}\) , \( -\frac{275}{23} a^{3} - \frac{13}{23} a^{2} + \frac{4015}{23} a + \frac{4082}{23}\bigr] \)
29.2-a2	\( \bigl[-\frac{4}{23} a^{3} + \frac{6}{23} a^{2} + \frac{63}{23} a - \frac{21}{23}\) , \( -\frac{1}{23} a^{3} - \frac{10}{23} a^{2} + \frac{33}{23} a + \frac{104}{23}\) , \( -\frac{2}{23} a^{3} + \frac{3}{23} a^{2} + \frac{43}{23} a + \frac{1}{23}\) , \( \frac{17}{23} a^{3} - \frac{106}{23} a^{2} - \frac{147}{23} a + \frac{1153}{23}\) , \( -\frac{160}{23} a^{3} + \frac{424}{23} a^{2} + \frac{1922}{23} a - \frac{3577}{23}\bigr] \)

Rank: \( 1 \)

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

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