Properties

Base field \(\Q(\sqrt{5}, \sqrt{6})\)
Label 4.4.14400.1-20.1-f
Conductor 20.1
Rank \( 1 \)

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

Isogeny class 20.1-f contains only one elliptic curve.

Curve label Weierstrass Coefficients
20.1-f1 \( \bigl[-\frac{1}{19} a^{3} + \frac{11}{19} a^{2} + \frac{9}{19} a - 3\) , \( -\frac{1}{19} a^{3} + \frac{11}{19} a^{2} + \frac{9}{19} a - 5\) , \( -\frac{4}{19} a^{3} + \frac{6}{19} a^{2} + \frac{55}{19} a - 1\) , \( -\frac{259}{19} a^{3} + \frac{759}{19} a^{2} + \frac{2787}{19} a - 317\) , \( \frac{1891}{19} a^{3} - \frac{5316}{19} a^{2} - \frac{20097}{19} a + 2261\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph