Properties

Base field 4.4.19821.1
Label 4.4.19821.1-47.1-a
Conductor 47.1
Rank \( 1 \)

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 47.1-a over 4.4.19821.1

Isogeny class 47.1-a contains only one elliptic curve.

Curve label Weierstrass Coefficients
47.1-a1 \( \bigl[\frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 2 a\) , \( \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 3 a - 2\) , \( 1\) , \( -\frac{1}{3} a^{3} + \frac{2}{3} a^{2} + 4 a + 1\) , \( \frac{1}{3} a^{3} + \frac{1}{3} a^{2} - 2 a - 1\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph