Properties

Base field 5.5.65657.1
Label 5.5.65657.1-27.1-d
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-d over 5.5.65657.1

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

Curve label Weierstrass Coefficients
27.1-d1 \( \bigl[a^{2} - 2\) , \( -a^{4} + 5 a^{2} - 2\) , \( a^{2} - a - 1\) , \( 3 a^{4} - 9 a^{3} - 7 a^{2} + 21 a + 2\) , \( 9 a^{4} - 15 a^{3} - 40 a^{2} + 52 a + 13\bigr] \)
27.1-d2 \( \bigl[-a^{4} + a^{3} + 5 a^{2} - 3 a - 3\) , \( a^{4} - a^{3} - 5 a^{2} + 3 a + 4\) , \( a^{2} - a - 2\) , \( -2 a^{2} + 3 a + 4\) , \( -2 a^{4} - 2 a^{3} + 10 a^{2} + 12 a + 3\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

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

Isogeny graph