Properties

Base field 4.4.8789.1
Label 4.4.8789.1-17.3-a
Conductor 17.3
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 17.3-a over 4.4.8789.1

Isogeny class 17.3-a contains only one elliptic curve.

Curve label Weierstrass Coefficients
17.3-a1 \( \bigl[a\) , \( 2 a^{3} - 3 a^{2} - 9 a\) , \( 2 a^{3} - 3 a^{2} - 9 a - 1\) , \( 4 a^{3} - 5 a^{2} - 20 a - 3\) , \( 2 a^{3} - 2 a^{2} - 10 a - 5\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph