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

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

Isogeny class 20.2-a contains only one elliptic curve.

Curve label	Weierstrass Coefficients
20.2-a1	\( \bigl[-\frac{1}{19} a^{3} + \frac{11}{19} a^{2} + \frac{9}{19} a - 3\) , \( -\frac{1}{19} a^{3} + \frac{11}{19} a^{2} + \frac{9}{19} a - 5\) , \( -\frac{1}{19} a^{3} + \frac{11}{19} a^{2} - \frac{10}{19} a - 3\) , \( -\frac{91}{19} a^{3} - \frac{196}{19} a^{2} + \frac{439}{19} a + 23\) , \( \frac{325}{19} a^{3} + \frac{662}{19} a^{2} - \frac{1481}{19} a - 81\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{r} 1 \end{array}\right)\)

Isogeny graph