Properties

Base field 4.4.15952.1
Label 4.4.15952.1-9.1-a
Conductor 9.1
Rank \( 1 \)

Related objects

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Base field 4.4.15952.1

Generator \(a\), with minimal polynomial \( x^{4} - 6 x^{2} - 2 x + 1 \); class number \(1\).

Elliptic curves in class 9.1-a over 4.4.15952.1

Isogeny class 9.1-a contains 8 curves linked by isogenies of degrees dividing 12.

Curve label Weierstrass Coefficients
9.1-a1 \( \bigl[a^{2} - 3\) , \( a^{2} - 2 a - 3\) , \( -a^{3} + a^{2} + 6 a - 1\) , \( -4 a^{3} - 3 a^{2} + 5 a - 2\) , \( 3 a^{3} + 15 a^{2} + 12 a - 2\bigr] \)
9.1-a2 \( \bigl[a^{2} - 3\) , \( a^{3} - 7 a - 1\) , \( a^{2} - a - 3\) , \( 49 a^{3} - 63 a^{2} - 144 a - 49\) , \( -181 a^{3} + 533 a^{2} - 57 a - 298\bigr] \)
9.1-a3 \( \bigl[a^{2} - 3\) , \( a^{3} - 7 a - 1\) , \( 1\) , \( -38 a^{3} + 25 a^{2} + 209 a - 57\) , \( -264 a^{3} + 170 a^{2} + 1472 a - 413\bigr] \)
9.1-a4 \( \bigl[a^{2} - a - 2\) , \( -2 a^{3} + a^{2} + 11 a - 2\) , \( a^{3} - 6 a\) , \( 3 a^{3} - 2 a^{2} - 20 a + 5\) , \( a^{2}\bigr] \)
9.1-a5 \( \bigl[a^{2} - a - 2\) , \( -a\) , \( -a^{3} + a^{2} + 6 a - 1\) , \( -17 a^{3} - 16 a^{2} + 53 a + 33\) , \( 117 a^{3} + 77 a^{2} - 583 a - 377\bigr] \)
9.1-a6 \( \bigl[a^{3} - 6 a - 1\) , \( -2 a^{3} + a^{2} + 11 a - 1\) , \( -a^{3} + a^{2} + 6 a - 1\) , \( 32 a^{3} + 4 a^{2} - 191 a - 100\) , \( -118 a^{3} - 114 a^{2} + 460 a + 299\bigr] \)
9.1-a7 \( \bigl[a^{3} - 6 a - 1\) , \( 2 a^{3} - a^{2} - 10 a\) , \( a^{2} - 2\) , \( 8 a^{3} - 2 a^{2} - 46 a - 5\) , \( -2 a^{3} - 4 a^{2} + 12 a + 25\bigr] \)
9.1-a8 \( \bigl[a^{3} - 5 a\) , \( 2 a^{3} - a^{2} - 11 a\) , \( a^{3} - 6 a\) , \( 58 a^{3} + 13 a^{2} - 345 a - 198\) , \( 320 a^{3} + 85 a^{2} - 1900 a - 1158\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 3 & 2 & 2 & 6 & 6 & 2 & 6 \\ 3 & 1 & 6 & 6 & 2 & 2 & 6 & 2 \\ 2 & 6 & 1 & 4 & 12 & 12 & 4 & 3 \\ 2 & 6 & 4 & 1 & 3 & 12 & 4 & 12 \\ 6 & 2 & 12 & 3 & 1 & 4 & 12 & 4 \\ 6 & 2 & 12 & 12 & 4 & 1 & 3 & 4 \\ 2 & 6 & 4 & 4 & 12 & 3 & 1 & 12 \\ 6 & 2 & 3 & 12 & 4 & 4 & 12 & 1 \end{array}\right)\)

Isogeny graph