Properties

Base field 4.4.19025.1
Label 4.4.19025.1-20.2-b
Conductor 20.2
Rank \( 1 \)

Related objects

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Base field 4.4.19025.1

Generator \(a\), with minimal polynomial \( x^{4} - 2 x^{3} - 13 x^{2} + 14 x + 44 \); class number \(1\).

Elliptic curves in class 20.2-b over 4.4.19025.1

Isogeny class 20.2-b contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
20.2-b1 \( \bigl[\frac{1}{2} a^{3} - \frac{9}{2} a - 3\) , \( -\frac{1}{2} a^{2} - \frac{1}{2} a + 5\) , \( \frac{1}{2} a^{3} - \frac{9}{2} a - 4\) , \( -2 a^{3} - 5 a^{2} + 14 a + 38\) , \( 6 a^{3} + 8 a^{2} - 44 a - 63\bigr] \)
20.2-b2 \( \bigl[1\) , \( -\frac{1}{2} a^{2} - \frac{1}{2} a + 5\) , \( \frac{1}{2} a^{3} - \frac{7}{2} a - 4\) , \( -20 a^{3} + \frac{149}{2} a^{2} + \frac{259}{2} a - 501\) , \( \frac{239}{2} a^{3} - \frac{897}{2} a^{2} - 776 a + 3032\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph