Properties

Base field 4.4.17069.1
Label 4.4.17069.1-9.1-a
Conductor 9.1
Rank \( 1 \)

Related objects

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Base field 4.4.17069.1

Generator \(a\), with minimal polynomial \( x^{4} - x^{3} - 8 x^{2} - 4 x + 3 \); class number \(1\).

Elliptic curves in class 9.1-a over 4.4.17069.1

Isogeny class 9.1-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label Weierstrass Coefficients
9.1-a1 \( \bigl[a^{3} - a^{2} - 7 a - 3\) , \( -a^{3} + a^{2} + 7 a + 5\) , \( a^{3} - a^{2} - 6 a - 3\) , \( -6 a^{3} - a^{2} + 58 a + 55\) , \( -22 a^{3} + 24 a^{2} + 154 a + 105\bigr] \)
9.1-a2 \( \bigl[a^{3} - a^{2} - 7 a - 3\) , \( -a^{3} + a^{2} + 7 a + 5\) , \( a^{3} - a^{2} - 6 a - 3\) , \( 44 a^{3} - 136 a^{2} - 112 a + 140\) , \( -340 a^{3} + 890 a^{2} + 1215 a - 470\bigr] \)
9.1-a3 \( \bigl[a^{3} - 2 a^{2} - 5 a\) , \( a^{3} - 2 a^{2} - 6 a - 1\) , \( 0\) , \( 20 a^{3} - 44 a^{2} - 108 a + 44\) , \( 37 a^{3} - 83 a^{2} - 190 a + 103\bigr] \)
9.1-a4 \( \bigl[1\) , \( -a + 1\) , \( a^{3} - a^{2} - 7 a - 4\) , \( 4 a^{3} - 2 a^{2} - 34 a - 30\) , \( -20 a^{3} + 12 a^{2} + 164 a + 146\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 6 & 3 \\ 2 & 1 & 3 & 6 \\ 6 & 3 & 1 & 2 \\ 3 & 6 & 2 & 1 \end{array}\right)\)

Isogeny graph