Properties

Base field \(\Q(\sqrt{-3}) \)
Label 2.0.3.1-28224.3-c
Conductor 28224.3
Rank \( 1 \)

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 28224.3-c over \(\Q(\sqrt{-3}) \)

Isogeny class 28224.3-c contains 8 curves linked by isogenies of degrees dividing 16.

Curve label Weierstrass Coefficients
28224.3-c1 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -210 a + 171\) , \( 237 a - 1041\bigr] \)
28224.3-c2 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -180 a - 24\) , \( -1320 a + 480\bigr] \)
28224.3-c3 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -375 a + 141\) , \( 10281 a + 9084\bigr] \)
28224.3-c4 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -15 a + 6\) , \( -24 a - 6\bigr] \)
28224.3-c5 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 105 a - 39\) , \( -99 a - 180\bigr] \)
28224.3-c6 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 585 a - 219\) , \( 2961 a + 1980\bigr] \)
28224.3-c7 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 1545 a - 579\) , \( -11079 a - 10836\bigr] \)
28224.3-c8 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 9225 a - 3459\) , \( 179001 a + 143676\bigr] \)

Rank

Rank: \( 1 \)

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