Properties

Base field 4.4.19821.1
Label 4.4.19821.1-17.1-a
Conductor 17.1
Rank not recorded

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Base field 4.4.19821.1

Generator \(a\), with minimal polynomial \( x^{4} - x^{3} - 8 x^{2} + 6 x + 3 \); class number \(1\).

Elliptic curves in class 17.1-a over 4.4.19821.1

Isogeny class 17.1-a contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
17.1-a1 \( \bigl[a^{2} - a - 4\) , \( \frac{2}{3} a^{3} - \frac{1}{3} a^{2} - 4 a + 1\) , \( 0\) , \( 2 a^{3} - 17 a + 4\) , \( \frac{7}{3} a^{3} + \frac{1}{3} a^{2} - 20 a - 1\bigr] \)
17.1-a2 \( \bigl[a^{2} - a - 4\) , \( \frac{2}{3} a^{3} - \frac{1}{3} a^{2} - 4 a + 1\) , \( 0\) , \( \frac{1}{3} a^{3} - \frac{5}{3} a^{2} - 2 a + 9\) , \( \frac{19}{3} a^{3} - \frac{2}{3} a^{2} - 48 a - 11\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

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

Isogeny graph