Properties

Base field 6.6.434581.1
Label 6.6.434581.1-27.2-b
Conductor 27.2
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 27.2-b over 6.6.434581.1

Isogeny class 27.2-b contains only one elliptic curve.

Curve label Weierstrass Coefficients
27.2-b1 \( \bigl[a^{5} - 2 a^{4} - 3 a^{3} + 3 a^{2} + 2 a + 1\) , \( -3 a^{5} + 8 a^{4} + 6 a^{3} - 18 a^{2} + a + 6\) , \( 3 a^{5} - 6 a^{4} - 10 a^{3} + 12 a^{2} + 5 a - 2\) , \( 11 a^{5} - 13 a^{4} - 58 a^{3} + 16 a^{2} + 61 a + 21\) , \( -560 a^{5} + 744 a^{4} + 2735 a^{3} - 952 a^{2} - 2871 a - 825\bigr] \)

Rank

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Isogeny matrix

\(\left(\begin{array}{r} 1 \end{array}\right)\)

Isogeny graph