Properties

Base field 3.3.761.1
Label 3.3.761.1-27.1-f
Conductor 27.1
Rank \( 1 \)

Related objects

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Base field 3.3.761.1

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

Elliptic curves in class 27.1-f over 3.3.761.1

Isogeny class 27.1-f contains 4 curves linked by isogenies of degrees dividing 6.

Curve label Weierstrass Coefficients
27.1-f1 \( \bigl[a^{2} - 3\) , \( -a^{2} + 5\) , \( a^{2} - 4\) , \( 13 a^{2} - 16 a - 79\) , \( 92 a^{2} - 108 a - 533\bigr] \)
27.1-f2 \( \bigl[a^{2} - 3\) , \( -a^{2} + 5\) , \( a^{2} - 4\) , \( 8 a^{2} - a - 79\) , \( 102 a^{2} - 142 a - 525\bigr] \)
27.1-f3 \( \bigl[a\) , \( -a\) , \( a\) , \( -6 a - 11\) , \( a^{2} + 9 a + 13\bigr] \)
27.1-f4 \( \bigl[a\) , \( -a\) , \( a\) , \( -a - 1\) , \( 0\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 6 & 3 \\ 2 & 1 & 3 & 6 \\ 6 & 3 & 1 & 2 \\ 3 & 6 & 2 & 1 \end{array}\right)\)

Isogeny graph