Properties

Base field \(\Q(\sqrt{-3}) \)
Label 2.0.3.1-147.2-a
Conductor 147.2
Rank \( 0 \)

Related objects

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Base field \(\Q(\sqrt{-3}) \)

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

Elliptic curves in class 147.2-a over \(\Q(\sqrt{-3}) \)

Isogeny class 147.2-a contains 8 curves linked by isogenies of degrees dividing 16.

Curve label Weierstrass Coefficients
147.2-a1 \( \bigl[1\) , \( 0\) , \( 0\) , \( -470 a + 321\) , \( 1866 a - 3772\bigr] \)
147.2-a2 \( \bigl[1\) , \( 0\) , \( 0\) , \( 470 a - 149\) , \( -1866 a - 1906\bigr] \)
147.2-a3 \( \bigl[1\) , \( 0\) , \( 0\) , \( -34\) , \( -217\bigr] \)
147.2-a4 \( \bigl[1\) , \( 0\) , \( 0\) , \( 1\) , \( 0\bigr] \)
147.2-a5 \( \bigl[1\) , \( 0\) , \( 0\) , \( -4\) , \( -1\bigr] \)
147.2-a6 \( \bigl[1\) , \( 0\) , \( 0\) , \( -39\) , \( 90\bigr] \)
147.2-a7 \( \bigl[1\) , \( 0\) , \( 0\) , \( -49\) , \( -136\bigr] \)
147.2-a8 \( \bigl[1\) , \( 0\) , \( 0\) , \( -784\) , \( -8515\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 4 & 2 & 16 & 8 & 16 & 4 & 8 \\ 4 & 1 & 2 & 16 & 8 & 16 & 4 & 8 \\ 2 & 2 & 1 & 8 & 4 & 8 & 2 & 4 \\ 16 & 16 & 8 & 1 & 2 & 4 & 4 & 8 \\ 8 & 8 & 4 & 2 & 1 & 2 & 2 & 4 \\ 16 & 16 & 8 & 4 & 2 & 1 & 4 & 8 \\ 4 & 4 & 2 & 4 & 2 & 4 & 1 & 2 \\ 8 & 8 & 4 & 8 & 4 & 8 & 2 & 1 \end{array}\right)\)

Isogeny graph