Properties

Base field 3.3.321.1
Label 3.3.321.1-27.2-a
Conductor 27.2
Rank not recorded

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 27.2-a over 3.3.321.1

Isogeny class 27.2-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
27.2-a1 \( \bigl[a^{2} - a - 3\) , \( -a^{2} + 3\) , \( a^{2} - 2\) , \( 48 a^{2} - 17 a - 244\) , \( 487 a^{2} - 421 a - 1924\bigr] \)
27.2-a2 \( \bigl[a^{2} - a - 3\) , \( -a^{2} + 3\) , \( a^{2} - 2\) , \( -142 a^{2} + 383 a - 104\) , \( 1865 a^{2} - 5033 a + 1068\bigr] \)
27.2-a3 \( \bigl[a^{2} - a - 3\) , \( -a^{2} + 3\) , \( a^{2} - 2\) , \( -7 a^{2} + 23 a - 14\) , \( 38 a^{2} - 83 a - 30\bigr] \)
27.2-a4 \( \bigl[a^{2} - a - 3\) , \( -a^{2} + 3\) , \( a^{2} - 2\) , \( -2 a^{2} + 3 a + 6\) , \( -a^{2} - a + 4\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph