Properties

Base field 4.4.19821.1
Label 4.4.19821.1-57.1-f
Conductor 57.1
Rank not recorded

Related objects

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Base field 4.4.19821.1

Generator \(a\), with minimal polynomial \( x^{4} - x^{3} - 8 x^{2} + 6 x + 3 \); class number \(1\).

Elliptic curves in class 57.1-f over 4.4.19821.1

Isogeny class 57.1-f contains only one elliptic curve.

Curve label Weierstrass Coefficients
57.1-f1 \( \bigl[-\frac{1}{3} a^{3} + \frac{2}{3} a^{2} + 2 a - 3\) , \( \frac{2}{3} a^{3} - \frac{1}{3} a^{2} - 6 a + 3\) , \( a^{2} - a - 3\) , \( 2 a^{3} - 5 a^{2} - 13 a + 16\) , \( \frac{4}{3} a^{3} - \frac{14}{3} a^{2} - 12 a + 22\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

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

Isogeny graph