Properties

Base field 6.6.485125.1
Label 6.6.485125.1-9.1-a
Conductor 9.1
Rank \( 0 \)

Related objects

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Base field 6.6.485125.1

Generator \(a\), with minimal polynomial \( x^{6} - 2 x^{5} - 4 x^{4} + 8 x^{3} + 2 x^{2} - 5 x + 1 \); class number \(1\).

Elliptic curves in class 9.1-a over 6.6.485125.1

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

Curve label Weierstrass Coefficients
9.1-a1 \( \bigl[a^{4} - 3 a^{2} + 1\) , \( -a^{5} + 2 a^{4} + 4 a^{3} - 6 a^{2} - 3 a + 1\) , \( a^{5} - a^{4} - 4 a^{3} + 3 a^{2} + 2 a - 1\) , \( a^{5} - 8 a^{4} + 51 a^{3} - 29 a^{2} - 63 a + 5\) , \( 120 a^{5} - 261 a^{4} - 176 a^{3} + 398 a^{2} + 152 a - 73\bigr] \)
9.1-a2 \( \bigl[2 a^{5} - 2 a^{4} - 9 a^{3} + 7 a^{2} + 8 a - 3\) , \( -a^{4} + 4 a^{2} + a - 2\) , \( -a^{5} + 2 a^{4} + 4 a^{3} - 6 a^{2} - 2 a + 2\) , \( 14 a^{5} - 21 a^{4} - 69 a^{3} + 76 a^{2} + 74 a - 27\) , \( 61 a^{5} - 81 a^{4} - 299 a^{3} + 286 a^{2} + 316 a - 92\bigr] \)
9.1-a3 \( \bigl[-2 a^{5} + 3 a^{4} + 9 a^{3} - 10 a^{2} - 8 a + 3\) , \( -a^{3} + a^{2} + 3 a\) , \( a^{5} - a^{4} - 5 a^{3} + 4 a^{2} + 6 a - 1\) , \( 2 a^{5} + 6 a^{4} - 30 a^{3} - 14 a^{2} + 73 a - 17\) , \( -567 a^{5} + 1666 a^{4} + 714 a^{3} - 5224 a^{2} + 3738 a - 617\bigr] \)
9.1-a4 \( \bigl[2 a^{5} - 2 a^{4} - 9 a^{3} + 7 a^{2} + 8 a - 3\) , \( -a^{4} + 4 a^{2} + a - 2\) , \( -a^{5} + 2 a^{4} + 4 a^{3} - 6 a^{2} - 2 a + 2\) , \( -96 a^{5} + 119 a^{4} + 476 a^{3} - 414 a^{2} - 511 a + 108\) , \( 463 a^{5} - 597 a^{4} - 2282 a^{3} + 2083 a^{2} + 2445 a - 594\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph