Properties

Base field 5.5.36497.1
Label 5.5.36497.1-39.1-b
Conductor 39.1
Rank not recorded

Related objects

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Base field 5.5.36497.1

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

Elliptic curves in class 39.1-b over 5.5.36497.1

Isogeny class 39.1-b contains 8 curves linked by isogenies of degrees dividing 28.

Curve label Weierstrass Coefficients
39.1-b1 \( \bigl[2 a^{4} - 3 a^{3} - 6 a^{2} + 7 a + 1\) , \( a^{3} - a^{2} - 3 a + 2\) , \( 2 a^{4} - 3 a^{3} - 6 a^{2} + 7 a + 2\) , \( -324 a^{4} + 554 a^{3} + 1092 a^{2} - 1175 a - 803\) , \( -4619 a^{4} + 7541 a^{3} + 16214 a^{2} - 16147 a - 11168\bigr] \)
39.1-b2 \( \bigl[a^{4} - a^{3} - 3 a^{2} + 2 a + 1\) , \( -2 a^{4} + 3 a^{3} + 7 a^{2} - 7 a - 3\) , \( a^{4} - 2 a^{3} - 2 a^{2} + 4 a\) , \( -4 a^{4} + 10 a^{3} - a^{2} + 8 a - 21\) , \( 38 a^{4} - 121 a^{3} + 60 a^{2} + 31 a + 19\bigr] \)
39.1-b3 \( \bigl[2 a^{4} - 3 a^{3} - 6 a^{2} + 7 a + 1\) , \( a^{3} - a^{2} - 3 a + 2\) , \( 2 a^{4} - 3 a^{3} - 6 a^{2} + 7 a + 2\) , \( -4 a^{4} + 9 a^{3} + 12 a^{2} - 20 a - 3\) , \( 2 a^{4} - 9 a^{2} + 10\bigr] \)
39.1-b4 \( \bigl[a^{2} - a - 1\) , \( -a^{2} + a + 2\) , \( a^{2} - a - 1\) , \( 8 a^{4} - 20 a^{3} - 18 a^{2} + 50 a - 15\) , \( -5 a^{4} + 14 a^{3} + 10 a^{2} - 35 a + 12\bigr] \)
39.1-b5 \( \bigl[a^{4} - a^{3} - 4 a^{2} + 2 a + 2\) , \( -a^{4} + 2 a^{3} + 4 a^{2} - 5 a - 3\) , \( a^{4} - 2 a^{3} - 2 a^{2} + 4 a\) , \( 120 a^{4} - 100 a^{3} - 445 a^{2} + 30 a + 42\) , \( 665 a^{4} - 538 a^{3} - 2479 a^{2} + 223 a + 422\bigr] \)
39.1-b6 \( \bigl[2 a^{4} - 3 a^{3} - 6 a^{2} + 7 a + 1\) , \( a^{3} - a^{2} - 3 a + 2\) , \( 2 a^{4} - 3 a^{3} - 6 a^{2} + 7 a + 2\) , \( -4889 a^{4} + 8124 a^{3} + 17837 a^{2} - 18525 a - 13048\) , \( -269334 a^{4} + 434813 a^{3} + 983058 a^{2} - 970083 a - 674066\bigr] \)
39.1-b7 \( \bigl[a^{2} - a - 1\) , \( -a^{2} + a + 2\) , \( a^{2} - a - 1\) , \( 10238 a^{4} - 25455 a^{3} - 18068 a^{2} + 59680 a - 20375\) , \( 897162 a^{4} - 2245513 a^{3} - 1558277 a^{2} + 5265005 a - 1771850\bigr] \)
39.1-b8 \( \bigl[a^{4} - 2 a^{3} - 3 a^{2} + 5 a + 2\) , \( -a^{4} + 2 a^{3} + 2 a^{2} - 5 a\) , \( a^{4} - 2 a^{3} - 3 a^{2} + 5 a + 2\) , \( 22858 a^{4} - 15206 a^{3} - 89524 a^{2} - 4349 a + 16767\) , \( 2975973 a^{4} - 1981540 a^{3} - 11583514 a^{2} - 559230 a + 2228472\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 28 & 7 & 14 & 28 & 2 & 4 & 4 \\ 28 & 1 & 4 & 2 & 4 & 14 & 7 & 28 \\ 7 & 4 & 1 & 2 & 4 & 14 & 28 & 28 \\ 14 & 2 & 2 & 1 & 2 & 7 & 14 & 14 \\ 28 & 4 & 4 & 2 & 1 & 14 & 28 & 7 \\ 2 & 14 & 14 & 7 & 14 & 1 & 2 & 2 \\ 4 & 7 & 28 & 14 & 28 & 2 & 1 & 4 \\ 4 & 28 & 28 & 14 & 7 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph