Properties

Base field 4.4.8789.1
Label 4.4.8789.1-17.2-a
Conductor 17.2
Rank \( 0 \)

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 17.2-a over 4.4.8789.1

Isogeny class 17.2-a contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
17.2-a1 \( \bigl[a + 1\) , \( a^{2} - 2 a - 3\) , \( a^{3} - a^{2} - 5 a - 1\) , \( -4 a^{3} - 9 a^{2} + 4\) , \( -6 a^{3} - 12 a^{2} - 3 a + 1\bigr] \)
17.2-a2 \( \bigl[a + 1\) , \( a^{2} - 2 a - 3\) , \( a^{3} - a^{2} - 5 a - 1\) , \( -4 a^{3} - 4 a^{2} + 5 a + 4\) , \( -16 a^{3} - 34 a^{2} - 11 a + 3\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph