Properties

Base field \(\Q(\sqrt{5}, \sqrt{6})\)
Label 4.4.14400.1-20.1-h
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-h over \(\Q(\sqrt{5}, \sqrt{6})\)

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

Curve label Weierstrass Coefficients
20.1-h1 \( \bigl[-\frac{2}{19} a^{3} + \frac{3}{19} a^{2} + \frac{37}{19} a\) , \( 0\) , \( 0\) , \( -\frac{234}{19} a^{3} + \frac{351}{19} a^{2} + \frac{4329}{19} a - 409\) , \( -\frac{2222}{19} a^{3} + \frac{3333}{19} a^{2} + \frac{41107}{19} a - 3849\bigr] \)
20.1-h2 \( \bigl[-\frac{2}{19} a^{3} + \frac{3}{19} a^{2} + \frac{37}{19} a\) , \( 0\) , \( 0\) , \( -\frac{4}{19} a^{3} + \frac{6}{19} a^{2} + \frac{74}{19} a - 4\) , \( -\frac{4}{19} a^{3} + \frac{6}{19} a^{2} + \frac{74}{19} a - 6\bigr] \)
20.1-h3 \( \bigl[-\frac{2}{19} a^{3} + \frac{3}{19} a^{2} + \frac{37}{19} a\) , \( 0\) , \( 0\) , \( \frac{16}{19} a^{3} - \frac{24}{19} a^{2} - \frac{296}{19} a + 31\) , \( \frac{4}{19} a^{3} - \frac{6}{19} a^{2} - \frac{74}{19} a + 9\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph