Elliptic curve isogeny class 5.2-b over number field \(\Q(\sqrt{5}, \sqrt{6})\)

• Base field: \(\Q(\sqrt{5}, \sqrt{6})\)
• Label: 4.4.14400.1-5.2-b
• Conductor: 5.2
• Rank: \( 1 \)

Base field \(\Q(\sqrt{5}, \sqrt{6})\)

Generator \(a\), with minimal polynomial \( x^{4} - 2 x^{3} - 13 x^{2} + 14 x + 19 \); class number \(1\).

Elliptic curves in class 5.2-b over \(\Q(\sqrt{5}, \sqrt{6})\)

Isogeny class 5.2-b contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
5.2-b1	\( \bigl[-\frac{2}{19} a^{3} + \frac{3}{19} a^{2} + \frac{37}{19} a - 1\) , \( \frac{3}{19} a^{3} - \frac{14}{19} a^{2} - \frac{27}{19} a + 6\) , \( \frac{1}{19} a^{3} + \frac{8}{19} a^{2} - \frac{28}{19} a - 2\) , \( -\frac{320}{19} a^{3} + \frac{24}{19} a^{2} + \frac{4267}{19} a + 197\) , \( -\frac{2845}{19} a^{3} + \frac{439}{19} a^{2} + \frac{37917}{19} a + 1576\bigr] \)
5.2-b2	\( \bigl[-\frac{2}{19} a^{3} + \frac{3}{19} a^{2} + \frac{37}{19} a - 1\) , \( -\frac{1}{19} a^{3} - \frac{8}{19} a^{2} + \frac{9}{19} a + 2\) , \( -\frac{1}{19} a^{3} + \frac{11}{19} a^{2} + \frac{9}{19} a - 3\) , \( \frac{32}{19} a^{3} - \frac{181}{19} a^{2} + \frac{130}{19} a + 12\) , \( -\frac{177}{19} a^{3} + \frac{902}{19} a^{2} - \frac{440}{19} a - 59\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph