Properties

Base field 4.4.10025.1
Label 4.4.10025.1-20.1-f
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-f over 4.4.10025.1

Isogeny class 20.1-f contains only one elliptic curve.

Curve label Weierstrass Coefficients
20.1-f1 \( \bigl[\frac{1}{2} a^{3} + \frac{3}{2} a^{2} - \frac{7}{2} a - 7\) , \( -a^{2} + a + 5\) , \( 1\) , \( 3 a^{3} - 9 a^{2} - 2 a + 16\) , \( -\frac{43}{2} a^{3} + \frac{177}{2} a^{2} - \frac{53}{2} a - 149\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph