Properties

Base field 5.5.65657.1
Label 5.5.65657.1-27.1-e
Conductor 27.1
Rank not recorded

Related objects

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Base field 5.5.65657.1

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

Elliptic curves in class 27.1-e over 5.5.65657.1

Isogeny class 27.1-e contains only one elliptic curve.

Curve label Weierstrass Coefficients
27.1-e1 \( \bigl[-a^{4} + a^{3} + 5 a^{2} - 2 a - 3\) , \( -a^{4} + 2 a^{3} + 3 a^{2} - 4 a\) , \( -a^{4} + 2 a^{3} + 5 a^{2} - 6 a - 4\) , \( 2 a^{4} - 8 a^{3} + 5 a^{2} + 6 a + 1\) , \( -2 a^{4} + 5 a^{3} + a^{2} - 5 a - 1\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

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

Isogeny graph