Properties

Base field 4.4.8789.1
Label 4.4.8789.1-29.2-a
Conductor 29.2
Rank \( 1 \)

Related objects

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Base field 4.4.8789.1

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

Elliptic curves in class 29.2-a over 4.4.8789.1

Isogeny class 29.2-a contains only one elliptic curve.

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

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph