Properties

Base field 5.5.81509.1
Label 5.5.81509.1-16.2-b
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-b over 5.5.81509.1

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

Curve label Weierstrass Coefficients
16.2-b1 \( \bigl[a^{4} - a^{3} - 4 a^{2} + 3 a + 2\) , \( a^{3} - 2 a - 1\) , \( a^{4} - 5 a^{2} - a + 4\) , \( 3 a^{4} - 4 a^{3} - 7 a^{2} + 12 a - 4\) , \( -2 a^{4} + 6 a^{3} + 7 a^{2} - 15 a + 1\bigr] \)
16.2-b2 \( \bigl[a^{2} - 2\) , \( -a^{2} + a + 1\) , \( a^{4} - 4 a^{2} + 2\) , \( -2 a^{3} - a^{2} + 3 a + 1\) , \( -a^{4} - a^{3} + 2 a^{2} + a - 1\bigr] \)
16.2-b3 \( \bigl[a^{4} - a^{3} - 3 a^{2} + 3 a\) , \( a^{3} - 2 a - 2\) , \( a\) , \( 13 a^{4} - 20 a^{3} - 31 a^{2} + 56 a - 15\) , \( -18 a^{4} + 53 a^{3} + 45 a^{2} - 136 a + 43\bigr] \)
16.2-b4 \( \bigl[a^{3} - a^{2} - 2 a + 2\) , \( -a^{4} + 2 a^{3} + 4 a^{2} - 5 a - 4\) , \( a^{3} - 3 a\) , \( 3 a^{4} - 3 a^{3} - 18 a^{2} + 4 a + 9\) , \( -12 a^{4} - 4 a^{3} + 40 a^{2} + 17 a - 15\bigr] \)

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