Properties

Base field 5.5.65657.1
Label 5.5.65657.1-27.1-f
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-f over 5.5.65657.1

Isogeny class 27.1-f contains only one elliptic curve.

Curve label Weierstrass Coefficients
27.1-f1 \( \bigl[a^{3} - 3 a - 1\) , \( -3 a^{4} + 4 a^{3} + 13 a^{2} - 10 a - 10\) , \( -2 a^{4} + 3 a^{3} + 9 a^{2} - 8 a - 7\) , \( 2 a^{4} - 3 a^{3} - 12 a^{2} + 12 a + 19\) , \( -8 a^{4} + 9 a^{3} + 37 a^{2} - 21 a - 25\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

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

Isogeny graph