Properties

Base field \(\Q(\sqrt{-3}) \)
Label 2.0.3.1-112896.2-ba
Conductor 112896.2
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 112896.2-ba over \(\Q(\sqrt{-3}) \)

Isogeny class 112896.2-ba contains 10 curves linked by isogenies of degrees dividing 18.

Curve label Weierstrass Coefficients
112896.2-ba1 \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -8184 a\) , \( 335520 a - 167760\bigr] \)
112896.2-ba2 \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -24 a\) , \( -96 a + 48\bigr] \)
112896.2-ba3 \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 216 a\) , \( 2208 a - 1104\bigr] \)
112896.2-ba4 \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -1704 a\) , \( 26784 a - 13392\bigr] \)
112896.2-ba5 \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 8856 a + 11040\) , \( 670368 a - 876624\bigr] \)
112896.2-ba6 \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 19896 a - 11040\) , \( 670368 a + 206256\bigr] \)
112896.2-ba7 \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -504 a\) , \( -4704 a + 2352\bigr] \)
112896.2-ba8 \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 8856 a + 10560\) , \( 727200 a - 916560\bigr] \)
112896.2-ba9 \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 19416 a - 10560\) , \( 727200 a + 189360\bigr] \)
112896.2-ba10 \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -131064 a\) , \( 21175968 a - 10587984\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrrrr} 1 & 9 & 3 & 6 & 18 & 18 & 18 & 9 & 9 & 2 \\ 9 & 1 & 3 & 6 & 18 & 18 & 2 & 9 & 9 & 18 \\ 3 & 3 & 1 & 2 & 6 & 6 & 6 & 3 & 3 & 6 \\ 6 & 6 & 2 & 1 & 3 & 3 & 3 & 6 & 6 & 3 \\ 18 & 18 & 6 & 3 & 1 & 9 & 9 & 2 & 18 & 9 \\ 18 & 18 & 6 & 3 & 9 & 1 & 9 & 18 & 2 & 9 \\ 18 & 2 & 6 & 3 & 9 & 9 & 1 & 18 & 18 & 9 \\ 9 & 9 & 3 & 6 & 2 & 18 & 18 & 1 & 9 & 18 \\ 9 & 9 & 3 & 6 & 18 & 2 & 18 & 9 & 1 & 18 \\ 2 & 18 & 6 & 3 & 9 & 9 & 9 & 18 & 18 & 1 \end{array}\right)\)

Isogeny graph