Properties

Base field 5.5.160801.1
Label 5.5.160801.1-27.3-d
Conductor 27.3
Rank not recorded

Related objects

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Base field 5.5.160801.1

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

Elliptic curves in class 27.3-d over 5.5.160801.1

Isogeny class 27.3-d contains 2 curves linked by isogenies of degree 3.

Curve label Weierstrass Coefficients
27.3-d1 \( \bigl[a^{4} - a^{3} - 4 a^{2} + 4 a + 1\) , \( 2 a^{4} - a^{3} - 11 a^{2} + 4 a + 5\) , \( a^{4} - a^{3} - 4 a^{2} + 5 a\) , \( -27 a^{4} + 45 a^{3} + 102 a^{2} - 181 a + 52\) , \( -189 a^{4} + 319 a^{3} + 727 a^{2} - 1260 a + 290\bigr] \)
27.3-d2 \( \bigl[a^{4} - 4 a^{2} + a\) , \( a^{4} - a^{3} - 6 a^{2} + 3 a + 3\) , \( 1\) , \( 3 a^{4} - 14 a^{2} - 2 a + 5\) , \( 8 a^{4} + 2 a^{3} - 37 a^{2} - 13 a + 7\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

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

Isogeny graph