Elliptic curve isogeny class 20.2-b over number field \(\Q(\sqrt{5}, \sqrt{6})\)

• Base field: \(\Q(\sqrt{5}, \sqrt{6})\)
• Label: 4.4.14400.1-20.2-b
• Conductor: 20.2
• 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 20.2-b over \(\Q(\sqrt{5}, \sqrt{6})\)

Isogeny class 20.2-b contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
20.2-b1	\( \bigl[\frac{1}{19} a^{3} + \frac{8}{19} a^{2} - \frac{28}{19} a - 2\) , \( \frac{1}{19} a^{3} - \frac{11}{19} a^{2} - \frac{9}{19} a + 3\) , \( 0\) , \( \frac{231}{19} a^{3} + \frac{461}{19} a^{2} - \frac{1034}{19} a - 52\) , \( \frac{1420}{19} a^{3} + \frac{2943}{19} a^{2} - \frac{6510}{19} a - 348\bigr] \)
20.2-b2	\( \bigl[\frac{1}{19} a^{3} + \frac{8}{19} a^{2} - \frac{28}{19} a - 2\) , \( -\frac{2}{19} a^{3} + \frac{3}{19} a^{2} + \frac{37}{19} a - 2\) , \( \frac{1}{19} a^{3} + \frac{8}{19} a^{2} - \frac{28}{19} a - 2\) , \( -\frac{4}{19} a^{3} + \frac{44}{19} a^{2} + \frac{36}{19} a - 32\) , \( \frac{936}{19} a^{3} - \frac{2677}{19} a^{2} - \frac{9925}{19} a + 1140\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph