Properties

Base field 6.6.434581.1
Label 6.6.434581.1-1.1-a
Conductor 1.1
Rank not recorded

Related objects

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Base field 6.6.434581.1

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

Elliptic curves in class 1.1-a over 6.6.434581.1

Isogeny class 1.1-a contains 4 curves linked by isogenies of degrees dividing 39.

Curve label Weierstrass Coefficients
1.1-a1 \( \bigl[3 a^{5} - 7 a^{4} - 8 a^{3} + 15 a^{2} + a - 3\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 2 a + 2\) , \( 2 a^{5} - 5 a^{4} - 5 a^{3} + 12 a^{2} - 3\) , \( -2015 a^{5} + 2317 a^{4} + 10491 a^{3} - 2078 a^{2} - 11628 a - 4340\) , \( -87669 a^{5} + 112368 a^{4} + 435832 a^{3} - 134018 a^{2} - 464939 a - 144427\bigr] \)
1.1-a2 \( \bigl[2 a^{5} - 4 a^{4} - 6 a^{3} + 7 a^{2} + a - 1\) , \( a^{5} - 4 a^{4} + 11 a^{2} - 2 a - 3\) , \( 2 a^{5} - 4 a^{4} - 6 a^{3} + 7 a^{2} + 2 a\) , \( 670 a^{5} - 2194 a^{4} + 16 a^{3} + 3065 a^{2} - 90 a - 1279\) , \( 20194 a^{5} - 68427 a^{4} + 14638 a^{3} + 73555 a^{2} - 10467 a - 21619\bigr] \)
1.1-a3 \( \bigl[3 a^{5} - 7 a^{4} - 8 a^{3} + 15 a^{2} + a - 4\) , \( a^{5} - 3 a^{4} - 2 a^{3} + 8 a^{2} - 3\) , \( a^{5} - 3 a^{4} - 2 a^{3} + 8 a^{2} - 2\) , \( -3 a^{4} + 4 a^{3} + 12 a^{2} - 3 a - 4\) , \( 10 a^{5} - 28 a^{4} - 19 a^{3} + 67 a^{2} - 8 a - 15\bigr] \)
1.1-a4 \( \bigl[2 a^{5} - 4 a^{4} - 7 a^{3} + 8 a^{2} + 4 a - 1\) , \( a^{5} - 3 a^{4} - 2 a^{3} + 8 a^{2} - 4\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 3 a + 1\) , \( -3 a^{5} + 4 a^{4} + 15 a^{3} - 6 a^{2} - 17 a - 3\) , \( 3 a^{5} - 4 a^{4} - 15 a^{3} + 5 a^{2} + 16 a + 4\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 13 & 39 \\ 3 & 1 & 39 & 13 \\ 13 & 39 & 1 & 3 \\ 39 & 13 & 3 & 1 \end{array}\right)\)

Isogeny graph