Properties

Base field 4.4.5744.1
Label 4.4.5744.1-16.1-b
Conductor 16.1
Rank \( 0 \)

Related objects

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Base field 4.4.5744.1

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

Elliptic curves in class 16.1-b over 4.4.5744.1

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

Curve label Weierstrass Coefficients
16.1-b1 \( \bigl[a^{3} - 4 a - 1\) , \( a^{2} - a - 1\) , \( -a^{3} + a^{2} + 5 a\) , \( -39 a^{3} + 15 a^{2} + 144 a - 48\) , \( 144 a^{3} - 58 a^{2} - 562 a + 157\bigr] \)
16.1-b2 \( \bigl[a^{3} - 4 a - 1\) , \( -a^{2} + a + 3\) , \( a^{2} - a - 1\) , \( 9 a^{3} - 7 a^{2} - 38 a - 19\) , \( -17 a^{3} + 25 a^{2} + 45 a + 13\bigr] \)
16.1-b3 \( \bigl[a^{3} - 4 a - 1\) , \( -a^{2} + a + 3\) , \( a^{2} - a - 1\) , \( 4 a^{3} - 7 a^{2} - 8 a + 1\) , \( -9 a^{3} + 23 a^{2} + 2 a - 15\bigr] \)
16.1-b4 \( \bigl[0\) , \( -2 a^{3} + a^{2} + 9 a + 1\) , \( 0\) , \( -8 a^{3} - 22 a^{2} - 8 a + 9\) , \( 50 a^{3} + 122 a^{2} + 39 a - 21\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph