Properties

Base field 6.6.1387029.1
Label 6.6.1387029.1-27.1-m
Conductor 27.1
Rank \( 1 \)

Related objects

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Base field 6.6.1387029.1

Generator \(a\), with minimal polynomial \( x^{6} - 3 x^{5} - 2 x^{4} + 9 x^{3} - x^{2} - 4 x + 1 \); class number \(1\).

Elliptic curves in class 27.1-m over 6.6.1387029.1

Isogeny class 27.1-m contains 2 curves linked by isogenies of degree 3.

Curve label Weierstrass Coefficients
27.1-m1 \( \bigl[-a^{5} + 2 a^{4} + 5 a^{3} - 6 a^{2} - 7 a + 3\) , \( -2 a^{5} + 4 a^{4} + 7 a^{3} - 10 a^{2} - 4 a + 3\) , \( -a^{5} + 2 a^{4} + 5 a^{3} - 6 a^{2} - 6 a + 2\) , \( -14 a^{5} + 30 a^{4} + 50 a^{3} - 79 a^{2} - 42 a + 16\) , \( -24 a^{5} + 52 a^{4} + 88 a^{3} - 142 a^{2} - 82 a + 31\bigr] \)
27.1-m2 \( \bigl[-2 a^{5} + 5 a^{4} + 6 a^{3} - 13 a^{2} - 4 a + 3\) , \( 2 a^{5} - 4 a^{4} - 8 a^{3} + 11 a^{2} + 6 a - 2\) , \( -a^{5} + 3 a^{4} + 2 a^{3} - 7 a^{2} - a + 2\) , \( 2 a^{5} - 3 a^{4} - 14 a^{3} + 14 a^{2} + 20 a - 8\) , \( -6 a^{5} + 13 a^{4} + 20 a^{3} - 29 a^{2} - 25 a + 8\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph