Properties

Base field 4.4.17069.1
Label 4.4.17069.1-17.4-a
Conductor 17.4
Rank \( 0 \)

Related objects

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Base field 4.4.17069.1

Generator \(a\), with minimal polynomial \( x^{4} - x^{3} - 8 x^{2} - 4 x + 3 \); class number \(1\).

Elliptic curves in class 17.4-a over 4.4.17069.1

Isogeny class 17.4-a contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
17.4-a1 \( \bigl[a^{2} - 2 a - 3\) , \( -a^{3} + 2 a^{2} + 6 a + 1\) , \( a^{3} - a^{2} - 6 a - 4\) , \( -2 a^{3} + 5 a^{2} + 7 a - 2\) , \( -2 a^{3} + 6 a^{2} + 3 a - 9\bigr] \)
17.4-a2 \( \bigl[a^{2} - 2 a - 3\) , \( -a^{3} + 2 a^{2} + 6 a + 1\) , \( a^{3} - a^{2} - 6 a - 4\) , \( 8 a^{3} - 25 a^{2} - 28 a + 18\) , \( -16 a^{3} + 33 a^{2} + 42 a - 27\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph