Properties

Base field 6.6.1397493.1
Label 6.6.1397493.1-27.1-n
Conductor 27.1
Rank \( 0 \)

Related objects

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Base field 6.6.1397493.1

Generator \(a\), with minimal polynomial \( x^{6} - 3 x^{5} - 3 x^{4} + 10 x^{3} + 3 x^{2} - 6 x + 1 \); class number \(1\).

Elliptic curves in class 27.1-n over 6.6.1397493.1

Isogeny class 27.1-n contains 3 curves linked by isogenies of degrees dividing 9.

Curve label Weierstrass Coefficients
27.1-n1 \( \bigl[a^{5} - 2 a^{4} - 5 a^{3} + 7 a^{2} + 8 a - 3\) , \( -a^{5} + 2 a^{4} + 7 a^{3} - 11 a^{2} - 11 a + 8\) , \( a + 1\) , \( 88 a^{5} - 247 a^{4} - 295 a^{3} + 791 a^{2} + 390 a - 424\) , \( -462 a^{5} + 1310 a^{4} + 1568 a^{3} - 4227 a^{2} - 2118 a + 2250\bigr] \)
27.1-n2 \( \bigl[a^{5} - 2 a^{4} - 5 a^{3} + 7 a^{2} + 8 a - 3\) , \( -a^{5} + 2 a^{4} + 7 a^{3} - 11 a^{2} - 11 a + 8\) , \( a + 1\) , \( -2 a^{5} + 8 a^{4} + 5 a^{3} - 24 a^{2} - 10 a + 11\) , \( a^{5} + a^{4} - 3 a^{3} - 8 a^{2} - 2 a + 4\bigr] \)
27.1-n3 \( \bigl[a^{5} - 2 a^{4} - 5 a^{3} + 7 a^{2} + 8 a - 3\) , \( -a^{5} + 2 a^{4} + 7 a^{3} - 11 a^{2} - 11 a + 8\) , \( a + 1\) , \( -12 a^{5} + 33 a^{4} + 35 a^{3} - 114 a^{2} - 55 a + 56\) , \( -41 a^{5} + 22 a^{4} + 140 a^{3} - 52 a^{2} - 98 a + 42\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph