Properties

Base field 4.4.18625.1
Label 4.4.18625.1-20.1-b
Conductor 20.1
Rank \( 1 \)

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Base field 4.4.18625.1

Generator \(a\), with minimal polynomial \( x^{4} - x^{3} - 14 x^{2} + 9 x + 41 \); class number \(1\).

Elliptic curves in class 20.1-b over 4.4.18625.1

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

Curve label Weierstrass Coefficients
20.1-b1 \( \bigl[\frac{1}{6} a^{3} + a^{2} - \frac{4}{3} a - \frac{41}{6}\) , \( -a^{2} - a + 6\) , \( \frac{1}{6} a^{3} - \frac{4}{3} a + \frac{1}{6}\) , \( 25 a^{3} - 73 a^{2} - 208 a + 583\) , \( -\frac{965}{3} a^{3} + 816 a^{2} + \frac{9913}{3} a - \frac{24872}{3}\bigr] \)
20.1-b2 \( \bigl[\frac{1}{6} a^{3} - \frac{1}{3} a + \frac{1}{6}\) , \( -\frac{1}{6} a^{3} + a^{2} + \frac{1}{3} a - \frac{49}{6}\) , \( \frac{1}{6} a^{3} - \frac{1}{3} a + \frac{7}{6}\) , \( \frac{15}{2} a^{3} + 35 a^{2} - 87 a - \frac{723}{2}\) , \( -\frac{671}{6} a^{3} - 103 a^{2} + \frac{3434}{3} a + \frac{7489}{6}\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph