Properties

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

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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-e over 4.4.19821.1

Isogeny class 57.1-e contains only one elliptic curve.

Curve label Weierstrass Coefficients
57.1-e1 \( \bigl[\frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 2 a\) , \( a^{2} - 2 a - 5\) , \( \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 3 a - 1\) , \( -\frac{1}{3} a^{3} + \frac{2}{3} a^{2} + 6\) , \( \frac{1}{3} a^{3} + \frac{4}{3} a^{2} - 4 a - 5\bigr] \)

Rank

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Isogeny matrix

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

Isogeny graph