Properties

Base field 5.5.81509.1
Label 5.5.81509.1-16.2-d
Conductor 16.2
Rank \( 0 \)

Related objects

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Base field 5.5.81509.1

Generator \(a\), with minimal polynomial \( x^{5} - x^{4} - 5 x^{3} + 3 x^{2} + 5 x - 2 \); class number \(1\).

Elliptic curves in class 16.2-d over 5.5.81509.1

Isogeny class 16.2-d contains 4 curves linked by isogenies of degrees dividing 6.

Curve label Weierstrass Coefficients
16.2-d1 \( \bigl[a^{2} - 2\) , \( a^{3} - a^{2} - 4 a\) , \( a^{3} - 2 a\) , \( 31 a^{4} + 7 a^{3} - 148 a^{2} - 89 a + 50\) , \( -231 a^{4} - 50 a^{3} + 1093 a^{2} + 636 a - 380\bigr] \)
16.2-d2 \( \bigl[a^{4} - a^{3} - 3 a^{2} + 2 a\) , \( a^{4} - 2 a^{3} - 2 a^{2} + 6 a\) , \( a^{2} + a - 2\) , \( -a^{4} + 5 a^{3} - 5 a + 3\) , \( 3 a^{4} - 4 a^{3} - 3 a^{2} + 6 a - 2\bigr] \)
16.2-d3 \( \bigl[a^{3} - a^{2} - 3 a + 2\) , \( a^{2} + a - 2\) , \( a^{2} - 2\) , \( -9 a^{4} + 6 a^{3} + 48 a^{2} - 9 a - 49\) , \( -20 a^{4} + 12 a^{3} + 107 a^{2} - 20 a - 111\bigr] \)
16.2-d4 \( \bigl[a^{4} - a^{3} - 4 a^{2} + 3 a + 2\) , \( a^{4} - 2 a^{3} - 4 a^{2} + 6 a + 4\) , \( a^{4} - 4 a^{2} + 2\) , \( 25 a^{4} - 118 a^{2} - 52 a + 49\) , \( -88 a^{4} + 382 a^{2} + 203 a - 117\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph