Elliptic curve isogeny class 29.1-b over number field \(\Q(\sqrt{5}, \sqrt{7})\)

• Base field: \(\Q(\sqrt{5}, \sqrt{7})\)
• Label: 4.4.19600.1-29.1-b
• Conductor: 29.1
• Rank: \( 1 \)

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 \(1\).

Elliptic curves in class 29.1-b over \(\Q(\sqrt{5}, \sqrt{7})\)

Isogeny class 29.1-b contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
29.1-b1	\( \bigl[-\frac{1}{23} a^{3} + \frac{13}{23} a^{2} + \frac{10}{23} a - \frac{80}{23}\) , \( \frac{1}{23} a^{3} + \frac{10}{23} a^{2} - \frac{10}{23} a - \frac{58}{23}\) , \( 0\) , \( 5 a^{2} - 3 a - 14\) , \( -\frac{71}{23} a^{3} + \frac{555}{23} a^{2} - \frac{279}{23} a - \frac{1126}{23}\bigr] \)
29.1-b2	\( \bigl[-\frac{1}{23} a^{3} + \frac{13}{23} a^{2} - \frac{13}{23} a - \frac{103}{23}\) , \( \frac{4}{23} a^{3} - \frac{6}{23} a^{2} - \frac{63}{23} a + \frac{21}{23}\) , \( -\frac{3}{23} a^{3} + \frac{16}{23} a^{2} + \frac{30}{23} a - \frac{125}{23}\) , \( \frac{51}{23} a^{3} + \frac{119}{23} a^{2} - \frac{349}{23} a - \frac{382}{23}\) , \( -\frac{157}{23} a^{3} - \frac{305}{23} a^{2} + \frac{926}{23} a + \frac{1079}{23}\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph