Properties

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

Isogeny class 112896.2-y contains 8 curves linked by isogenies of degrees dividing 16.

Curve label Weierstrass Coefficients
112896.2-y1 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -22559 a + 7153\) , \( -1105583 a + 1105056\bigr] \)
112896.2-y2 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( a + 1633\) , \( -81695 a + 41664\bigr] \)
112896.2-y3 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( a - 47\) , \( -47 a\bigr] \)
112896.2-y4 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( a + 193\) , \( -191 a + 192\bigr] \)
112896.2-y5 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 22561 a - 15407\) , \( -1083023 a - 14880\bigr] \)
112896.2-y6 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( a + 1873\) , \( 36433 a - 17280\bigr] \)
112896.2-y7 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( a + 2353\) , \( -49871 a + 26112\bigr] \)
112896.2-y8 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( a + 37633\) , \( -3232127 a + 1634880\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph