Properties

Base field 4.4.4752.1
Label 4.4.4752.1-39.1-a
Conductor 39.1
Rank \( 0 \)

Related objects

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Base field 4.4.4752.1

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

Elliptic curves in class 39.1-a over 4.4.4752.1

Isogeny class 39.1-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
39.1-a1 \( \bigl[a^{3} - 4 a\) , \( -a^{2} + 2\) , \( a^{3} - a^{2} - 2 a + 1\) , \( -a^{3} + 4 a^{2} + 19 a - 89\) , \( 22 a^{3} - 125 a^{2} + 144 a + 85\bigr] \)
39.1-a2 \( \bigl[a^{3} - 4 a\) , \( -a^{2} + 2\) , \( a^{3} - a^{2} - 2 a + 1\) , \( -a^{3} - 6 a^{2} + 34 a - 44\) , \( 4 a^{3} - 46 a^{2} + 147 a - 149\bigr] \)
39.1-a3 \( \bigl[a^{3} - 4 a\) , \( -a^{2} + 2\) , \( a^{3} - a^{2} - 2 a + 1\) , \( -a^{3} - a^{2} + 4 a + 1\) , \( -a^{3} + 6 a - 5\bigr] \)
39.1-a4 \( \bigl[1\) , \( a^{3} - a^{2} - 4 a + 1\) , \( a^{3} - a^{2} - 2 a + 1\) , \( -1385 a^{3} - 686 a^{2} + 2441 a + 527\) , \( 40164 a^{3} + 19914 a^{2} - 70813 a - 16170\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph