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

• Base field: \(\Q(\sqrt{5}, \sqrt{6})\)
• Label: 4.4.14400.1-20.2-d
• Conductor: 20.2
• Rank: \( 0 \)

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-d over \(\Q(\sqrt{5}, \sqrt{6})\)

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

Curve label	Weierstrass Coefficients
20.2-d1	\( \bigl[\frac{1}{19} a^{3} + \frac{8}{19} a^{2} - \frac{28}{19} a - 2\) , \( \frac{1}{19} a^{3} - \frac{11}{19} a^{2} - \frac{9}{19} a + 3\) , \( \frac{1}{19} a^{3} + \frac{8}{19} a^{2} - \frac{28}{19} a - 2\) , \( -\frac{518}{19} a^{3} - \frac{1104}{19} a^{2} + \frac{2344}{19} a + 130\) , \( -\frac{8969}{19} a^{3} - \frac{18571}{19} a^{2} + \frac{41125}{19} a + 2205\bigr] \)
20.2-d2	\( \bigl[-\frac{1}{19} a^{3} + \frac{11}{19} a^{2} + \frac{9}{19} a - 3\) , \( -\frac{1}{19} a^{3} - \frac{8}{19} a^{2} + \frac{28}{19} a + 2\) , \( 0\) , \( \frac{289}{19} a^{3} - \frac{1450}{19} a^{2} + \frac{743}{19} a + 94\) , \( \frac{3500}{19} a^{3} - \frac{17733}{19} a^{2} + \frac{8932}{19} a + 1139\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph