Elliptic curve isogeny class 20.1-e over number field \(\Q(\sqrt{5}, \sqrt{6})\)

• Base field: \(\Q(\sqrt{5}, \sqrt{6})\)
• Label: 4.4.14400.1-20.1-e
• Conductor: 20.1
• 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 20.1-e over \(\Q(\sqrt{5}, \sqrt{6})\)

Isogeny class 20.1-e contains 3 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
20.1-e1	\( \bigl[1\) , \( 0\) , \( 1\) , \( \frac{332}{19} a^{3} - \frac{498}{19} a^{2} - \frac{6142}{19} a - 247\) , \( -\frac{3654}{19} a^{3} + \frac{5481}{19} a^{2} + \frac{67599}{19} a + 2653\bigr] \)
20.1-e2	\( \bigl[1\) , \( 0\) , \( 1\) , \( \frac{2}{19} a^{3} - \frac{3}{19} a^{2} - \frac{37}{19} a - 2\) , \( -\frac{10}{19} a^{3} + \frac{15}{19} a^{2} + \frac{185}{19} a + 7\bigr] \)
20.1-e3	\( \bigl[1\) , \( 0\) , \( 1\) , \( -\frac{18}{19} a^{3} + \frac{27}{19} a^{2} + \frac{333}{19} a + 13\) , \( 14 a^{3} - 21 a^{2} - 259 a - 193\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph