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

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

Isogeny class 20.1-g contains only one elliptic curve.

Curve label	Weierstrass Coefficients
20.1-g1	\( \bigl[\frac{1}{19} a^{3} + \frac{8}{19} a^{2} - \frac{28}{19} a - 2\) , \( \frac{1}{19} a^{3} + \frac{8}{19} a^{2} - \frac{28}{19} a - 4\) , \( -\frac{3}{19} a^{3} + \frac{14}{19} a^{2} + \frac{27}{19} a - 4\) , \( \frac{64}{19} a^{3} + \frac{18}{19} a^{2} - \frac{937}{19} a - 43\) , \( \frac{221}{19} a^{3} + \frac{1}{19} a^{2} - \frac{3053}{19} a - 132\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph