Elliptic curve isogeny class 59.3-a over number field \(\Q(\sqrt{3}, \sqrt{5})\)

• Base field: \(\Q(\sqrt{3}, \sqrt{5})\)
• Label: 4.4.3600.1-59.3-a
• Conductor: 59.3
• Rank: \( 1 \)

Base field \(\Q(\sqrt{3}, \sqrt{5})\)

Generator \(a\), with minimal polynomial \( x^{4} - 2 x^{3} - 7 x^{2} + 8 x + 1 \); class number \(1\).

Elliptic curves in class 59.3-a over \(\Q(\sqrt{3}, \sqrt{5})\)

Isogeny class 59.3-a contains 2 curves linked by isogenies of degree 5.

Curve label	Weierstrass Coefficients
59.3-a1	\( \bigl[-\frac{4}{7} a^{3} + \frac{6}{7} a^{2} + \frac{31}{7} a - \frac{13}{7}\) , \( \frac{1}{7} a^{3} + \frac{2}{7} a^{2} - \frac{20}{7} a - \frac{2}{7}\) , \( \frac{1}{7} a^{3} + \frac{2}{7} a^{2} - \frac{13}{7} a - \frac{2}{7}\) , \( -\frac{17}{7} a^{3} - \frac{41}{7} a^{2} + \frac{74}{7} a + \frac{13}{7}\) , \( 2 a^{3} + 6 a^{2} - 9 a - 1\bigr] \)
59.3-a2	\( \bigl[-\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{19}{7} a - \frac{10}{7}\) , \( \frac{1}{7} a^{3} + \frac{2}{7} a^{2} - \frac{6}{7} a - \frac{16}{7}\) , \( -\frac{3}{7} a^{3} + \frac{8}{7} a^{2} + \frac{18}{7} a - \frac{22}{7}\) , \( -\frac{3}{7} a^{3} + \frac{8}{7} a^{2} + \frac{25}{7} a - \frac{36}{7}\) , \( \frac{15}{7} a^{3} - \frac{75}{7} a^{2} + \frac{92}{7} a - \frac{23}{7}\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph