Properties

Base field \(\Q(\sqrt{-3}) \)
Label 2.0.3.1-2352.2-b
Conductor 2352.2
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 2352.2-b over \(\Q(\sqrt{-3}) \)

Isogeny class 2352.2-b contains 8 curves linked by isogenies of degrees dividing 12.

Curve label Weierstrass Coefficients
2352.2-b1 \( \bigl[0\) , \( -a\) , \( 0\) , \( -113 a + 113\) , \( -516\bigr] \)
2352.2-b2 \( \bigl[0\) , \( -a\) , \( 0\) , \( -198 a + 13\) , \( -1525 a - 10\bigr] \)
2352.2-b3 \( \bigl[0\) , \( -a\) , \( 0\) , \( -13 a + 198\) , \( 1525 a - 1535\bigr] \)
2352.2-b4 \( \bigl[0\) , \( a - 1\) , \( 0\) , \( -7 a\) , \( 0\bigr] \)
2352.2-b5 \( \bigl[0\) , \( a - 1\) , \( 0\) , \( 28 a\) , \( -28\bigr] \)
2352.2-b6 \( \bigl[0\) , \( a - 1\) , \( 0\) , \( -67 a - 15\) , \( -285 a + 102\bigr] \)
2352.2-b7 \( \bigl[0\) , \( a - 1\) , \( 0\) , \( -82 a + 15\) , \( 285 a - 183\bigr] \)
2352.2-b8 \( \bigl[0\) , \( -a\) , \( 0\) , \( -1828 a + 1828\) , \( -30700\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 2 & 3 & 6 & 6 & 6 & 2 \\ 2 & 1 & 4 & 6 & 12 & 3 & 12 & 4 \\ 2 & 4 & 1 & 6 & 12 & 12 & 3 & 4 \\ 3 & 6 & 6 & 1 & 2 & 2 & 2 & 6 \\ 6 & 12 & 12 & 2 & 1 & 4 & 4 & 3 \\ 6 & 3 & 12 & 2 & 4 & 1 & 4 & 12 \\ 6 & 12 & 3 & 2 & 4 & 4 & 1 & 12 \\ 2 & 4 & 4 & 6 & 3 & 12 & 12 & 1 \end{array}\right)\)

Isogeny graph