Properties

Base field 4.4.13768.1
Label 4.4.13768.1-16.1-b
Conductor 16.1
Rank \( 1 \)

Related objects

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Base field 4.4.13768.1

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

Elliptic curves in class 16.1-b over 4.4.13768.1

Isogeny class 16.1-b contains 4 curves linked by isogenies of degrees dividing 6.

Curve label Weierstrass Coefficients
16.1-b1 \( \bigl[a^{3} - 4 a - 2\) , \( a^{3} - a^{2} - 5 a\) , \( a^{3} - a^{2} - 4 a + 2\) , \( 20 a^{3} - 2 a^{2} - 104 a - 55\) , \( -85 a^{3} + 17 a^{2} + 433 a + 180\bigr] \)
16.1-b2 \( \bigl[a^{2} - 2\) , \( -a^{3} + 6 a + 2\) , \( a^{3} - 4 a - 2\) , \( -a^{2} - 4 a - 2\) , \( -2 a^{3} - 5 a^{2} - 2 a\bigr] \)
16.1-b3 \( \bigl[a\) , \( a + 1\) , \( a^{3} - a^{2} - 4 a + 2\) , \( 3 a - 1\) , \( a^{3} - a^{2} - 3 a + 2\bigr] \)
16.1-b4 \( \bigl[a\) , \( -a^{3} + 6 a + 2\) , \( 0\) , \( -a^{3} - 2 a^{2} + 9 a + 5\) , \( -2 a^{3} + 5 a^{2} + 3 a\bigr] \)

Rank

Rank: \( 1 \)

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