Properties

Base field 6.6.1541581.1
Label 6.6.1541581.1-27.1-a
Conductor 27.1
Rank \( 0 \)

Related objects

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Base field 6.6.1541581.1

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

Elliptic curves in class 27.1-a over 6.6.1541581.1

Isogeny class 27.1-a contains only one elliptic curve.

Curve label Weierstrass Coefficients
27.1-a1 \( \bigl[2 a^{5} - 4 a^{4} - 7 a^{3} + 9 a^{2} + 5 a + 1\) , \( -a^{5} + 2 a^{4} + 4 a^{3} - 5 a^{2} - 4 a - 1\) , \( 2 a^{5} - 4 a^{4} - 7 a^{3} + 9 a^{2} + 5 a\) , \( 2 a^{5} - 3 a^{4} - 10 a^{3} + 9 a^{2} + 13 a - 7\) , \( 4 a^{5} - 7 a^{4} - 18 a^{3} + 20 a^{2} + 21 a - 8\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph