Properties

Base field 4.4.16317.1
Label 4.4.16317.1-1.1-a
Conductor 1.1
Rank \( 0 \)

Related objects

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Base field 4.4.16317.1

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

Elliptic curves in class 1.1-a over 4.4.16317.1

Isogeny class 1.1-a contains 4 curves linked by isogenies of degrees dividing 14.

Curve label Weierstrass Coefficients
1.1-a1 \( \bigl[a^{3} - 4 a - 2\) , \( a^{3} - 2 a^{2} - 2 a + 5\) , \( 0\) , \( 10 a^{3} - a^{2} - 29 a + 5\) , \( 12 a^{3} + 8 a^{2} - 22 a + 1\bigr] \)
1.1-a2 \( \bigl[a^{3} - 4 a - 2\) , \( a^{3} - 2 a^{2} - 2 a + 5\) , \( 0\) , \( 5 a^{3} + 4 a^{2} - 4 a + 10\) , \( 13 a^{3} + 10 a^{2} - 20 a + 3\bigr] \)
1.1-a3 \( \bigl[a^{3} - a^{2} - 3 a + 1\) , \( -a^{3} + a^{2} + 4 a - 2\) , \( a^{3} - a^{2} - 3 a + 1\) , \( -6 a^{3} + 10 a^{2} + 24 a - 31\) , \( 16 a^{3} - 36 a^{2} - 61 a + 95\bigr] \)
1.1-a4 \( \bigl[a^{3} - a^{2} - 3 a + 1\) , \( -a^{3} + a^{2} + 4 a - 2\) , \( a^{3} - a^{2} - 3 a + 1\) , \( -a^{3} + 4 a - 1\) , \( -a^{2} + 2\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 7 & 14 \\ 2 & 1 & 14 & 7 \\ 7 & 14 & 1 & 2 \\ 14 & 7 & 2 & 1 \end{array}\right)\)

Isogeny graph