Properties

Base field 4.4.10025.1
Label 4.4.10025.1-20.1-b
Conductor 20.1
Rank \( 1 \)

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Base field 4.4.10025.1

Generator \(a\), with minimal polynomial \( x^{4} - x^{3} - 11 x^{2} + 10 x + 20 \); class number \(1\).

Elliptic curves in class 20.1-b over 4.4.10025.1

Isogeny class 20.1-b contains 2 curves linked by isogenies of degree 5.

Curve label Weierstrass Coefficients
20.1-b1 \( \bigl[\frac{1}{2} a^{3} + \frac{3}{2} a^{2} - \frac{7}{2} a - 7\) , \( \frac{1}{2} a^{3} + \frac{3}{2} a^{2} - \frac{9}{2} a - 7\) , \( \frac{1}{2} a^{3} + \frac{3}{2} a^{2} - \frac{7}{2} a - 8\) , \( 375 a^{3} + 570 a^{2} - 2855 a - 3479\) , \( -\frac{13691}{2} a^{3} - \frac{18561}{2} a^{2} + \frac{104869}{2} a + 54734\bigr] \)
20.1-b2 \( \bigl[\frac{1}{2} a^{3} + \frac{3}{2} a^{2} - \frac{7}{2} a - 7\) , \( \frac{1}{2} a^{3} + \frac{3}{2} a^{2} - \frac{5}{2} a - 7\) , \( \frac{1}{2} a^{3} + \frac{3}{2} a^{2} - \frac{7}{2} a - 8\) , \( 13 a^{3} - 11 a^{2} - 100 a + 126\) , \( \frac{43}{2} a^{3} - \frac{3}{2} a^{2} - \frac{565}{2} a + 390\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph