Properties

Base field 3.3.321.1
Label 3.3.321.1-27.1-c
Conductor 27.1
Rank \( 1 \)

Related objects

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Base field 3.3.321.1

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

Elliptic curves in class 27.1-c over 3.3.321.1

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

Curve label Weierstrass Coefficients
27.1-c1 \( \bigl[a^{2} - 3\) , \( a^{2} - a - 4\) , \( a^{2} - 2\) , \( -141 a^{2} + 401 a - 138\) , \( 1980 a^{2} - 5420 a + 1345\bigr] \)
27.1-c2 \( \bigl[a^{2} - 3\) , \( a^{2} - a - 4\) , \( a^{2} - 2\) , \( -6 a^{2} + 16 a - 8\) , \( 50 a^{2} - 138 a + 33\bigr] \)
27.1-c3 \( \bigl[a + 1\) , \( a^{2} - 2\) , \( a^{2} - a - 2\) , \( 32 a^{2} + 2 a - 185\) , \( -130 a^{2} + 189 a + 334\bigr] \)
27.1-c4 \( \bigl[a + 1\) , \( a^{2} - 2\) , \( a^{2} - a - 2\) , \( -8 a^{2} + 7 a + 45\) , \( -4 a^{2} + 12 a + 7\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph