Elliptic curve isogeny class 576.1-c over number field \(\Q(\sqrt{3}, \sqrt{5})\)

• Base field: \(\Q(\sqrt{3}, \sqrt{5})\)
• Label: 4.4.3600.1-576.1-c
• Conductor: 576.1
• 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 576.1-c over \(\Q(\sqrt{3}, \sqrt{5})\)

Isogeny class 576.1-c contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
576.1-c1	\( \bigl[-\frac{1}{7} a^{3} + \frac{5}{7} a^{2} - \frac{1}{7} a - \frac{12}{7}\) , \( -\frac{1}{7} a^{3} - \frac{2}{7} a^{2} + \frac{6}{7} a + \frac{16}{7}\) , \( -\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{19}{7} a - \frac{3}{7}\) , \( \frac{17}{7} a^{3} - \frac{57}{7} a^{2} + \frac{52}{7} a + \frac{22}{7}\) , \( -\frac{65}{7} a^{3} + \frac{178}{7} a^{2} - \frac{114}{7} a - \frac{10}{7}\bigr] \)
576.1-c2	\( \bigl[-\frac{2}{7} a^{3} + \frac{3}{7} a^{2} + \frac{19}{7} a - \frac{3}{7}\) , \( -\frac{1}{7} a^{3} - \frac{2}{7} a^{2} + \frac{20}{7} a + \frac{16}{7}\) , \( 0\) , \( -3 a^{3} - 13 a^{2} - 17 a - 2\) , \( -\frac{426}{7} a^{3} - \frac{495}{7} a^{2} + \frac{1254}{7} a + \frac{138}{7}\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph