Properties

Base field \(\Q(\sqrt{-3}) \)
Label 2.0.3.1-192.1-a
Conductor 192.1
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 192.1-a over \(\Q(\sqrt{-3}) \)

Isogeny class 192.1-a contains 8 curves linked by isogenies of degrees dividing 16.

Curve label Weierstrass Coefficients
192.1-a1 \( \bigl[0\) , \( a\) , \( 0\) , \( 11 a - 6\) , \( 11 a - 1\bigr] \)
192.1-a2 \( \bigl[0\) , \( a\) , \( 0\) , \( 6 a - 11\) , \( -11 a + 10\bigr] \)
192.1-a3 \( \bigl[0\) , \( a\) , \( 0\) , \( 16 a - 16\) , \( -180\bigr] \)
192.1-a4 \( \bigl[0\) , \( a\) , \( 0\) , \( a - 1\) , \( 0\bigr] \)
192.1-a5 \( \bigl[0\) , \( a\) , \( 0\) , \( -4 a + 4\) , \( 4\bigr] \)
192.1-a6 \( \bigl[0\) , \( a\) , \( 0\) , \( -24 a + 24\) , \( -36\bigr] \)
192.1-a7 \( \bigl[0\) , \( a\) , \( 0\) , \( -64 a + 64\) , \( 220\bigr] \)
192.1-a8 \( \bigl[0\) , \( a\) , \( 0\) , \( -384 a + 384\) , \( -2772\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph