Properties

Base field 4.4.6809.1
Label 4.4.6809.1-17.1-a
Conductor 17.1
Rank \( 0 \)

Related objects

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Base field 4.4.6809.1

Generator \(a\), with minimal polynomial \( x^{4} - 5 x^{2} - x + 1 \); class number \(1\).

Elliptic curves in class 17.1-a over 4.4.6809.1

Isogeny class 17.1-a contains only one elliptic curve.

Curve label Weierstrass Coefficients
17.1-a1 \( \bigl[a^{3} - 4 a - 1\) , \( a^{3} - a^{2} - 4 a + 2\) , \( a^{3} - 5 a - 1\) , \( -45 a^{3} + 26 a^{2} + 208 a - 79\) , \( -308 a^{3} + 177 a^{2} + 1430 a - 528\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph