Properties

Base field \(\Q(\sqrt{5}, \sqrt{6})\)
Label 4.4.14400.1-20.1-d
Conductor 20.1
Rank \( 0 \)

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

Isogeny class 20.1-d contains 2 curves linked by isogenies of degree 3.

Curve label Weierstrass Coefficients
20.1-d1 \( \bigl[\frac{1}{19} a^{3} + \frac{8}{19} a^{2} - \frac{28}{19} a - 2\) , \( -\frac{2}{19} a^{3} + \frac{3}{19} a^{2} + \frac{37}{19} a - 2\) , \( \frac{1}{19} a^{3} + \frac{8}{19} a^{2} - \frac{28}{19} a - 2\) , \( -\frac{1404}{19} a^{3} + \frac{3968}{19} a^{2} + \frac{14992}{19} a - 1692\) , \( -\frac{24048}{19} a^{3} + \frac{68087}{19} a^{2} + \frac{256047}{19} a - 28928\bigr] \)
20.1-d2 \( \bigl[\frac{1}{19} a^{3} + \frac{8}{19} a^{2} - \frac{28}{19} a - 2\) , \( \frac{1}{19} a^{3} - \frac{11}{19} a^{2} - \frac{9}{19} a + 3\) , \( 0\) , \( -\frac{289}{19} a^{3} - \frac{583}{19} a^{2} + \frac{1290}{19} a + 72\) , \( -\frac{3500}{19} a^{3} - \frac{7233}{19} a^{2} + \frac{16034}{19} a + 860\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph