Properties

Base field 4.4.4913.1
Label 4.4.4913.1-16.1-a
Conductor 16.1
Rank \( 0 \)

Related objects

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Base field 4.4.4913.1

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

Elliptic curves in class 16.1-a over 4.4.4913.1

Isogeny class 16.1-a contains 4 curves linked by isogenies of degrees dividing 10.

Curve label Weierstrass Coefficients
16.1-a1 \( \bigl[\frac{1}{2} a^{3} - 3 a - \frac{3}{2}\) , \( -a^{2} + 2 a + 4\) , \( 0\) , \( -87 a^{3} + 104 a^{2} + 511 a - 250\) , \( -780 a^{3} + 1005 a^{2} + 4438 a - 2307\bigr] \)
16.1-a2 \( \bigl[\frac{1}{2} a^{3} - 3 a - \frac{3}{2}\) , \( -a^{2} + 2 a + 4\) , \( 0\) , \( -\frac{9}{2} a^{3} + 4 a^{2} + 26 a + \frac{5}{2}\) , \( -2 a^{3} + a^{2} + 12 a + 6\bigr] \)
16.1-a3 \( \bigl[a\) , \( -a^{2} + 3\) , \( \frac{1}{2} a^{3} - 3 a - \frac{3}{2}\) , \( \frac{113}{2} a^{3} - 11 a^{2} - 364 a - \frac{473}{2}\) , \( 551 a^{3} - 153 a^{2} - 3546 a - 1924\bigr] \)
16.1-a4 \( \bigl[a\) , \( -a^{2} + 3\) , \( \frac{1}{2} a^{3} - 3 a - \frac{3}{2}\) , \( \frac{3}{2} a^{3} - a^{2} - 9 a - \frac{3}{2}\) , \( \frac{1}{2} a^{3} - a^{2} - 3 a + \frac{5}{2}\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 5 & 2 & 10 \\ 5 & 1 & 10 & 2 \\ 2 & 10 & 1 & 5 \\ 10 & 2 & 5 & 1 \end{array}\right)\)

Isogeny graph