Properties

Base field \(\Q(\sqrt{-3}) \)
Label 2.0.3.1-75.1-a
Conductor 75.1
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 75.1-a over \(\Q(\sqrt{-3}) \)

Isogeny class 75.1-a contains 8 curves linked by isogenies of degrees dividing 16.

Curve label Weierstrass Coefficients
75.1-a1 \( \bigl[1\) , \( 1\) , \( 1\) , \( -110\) , \( -880\bigr] \)
75.1-a2 \( \bigl[1\) , \( 1\) , \( 1\) , \( 0\) , \( 0\bigr] \)
75.1-a3 \( \bigl[1\) , \( 1\) , \( 1\) , \( 35\) , \( -28\bigr] \)
75.1-a4 \( \bigl[1\) , \( 1\) , \( 1\) , \( -10\) , \( -10\bigr] \)
75.1-a5 \( \bigl[1\) , \( 1\) , \( 1\) , \( -5\) , \( 2\bigr] \)
75.1-a6 \( \bigl[1\) , \( 1\) , \( 1\) , \( -135\) , \( -660\bigr] \)
75.1-a7 \( \bigl[1\) , \( 1\) , \( 1\) , \( -80\) , \( 242\bigr] \)
75.1-a8 \( \bigl[1\) , \( 1\) , \( 1\) , \( -2160\) , \( -39540\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph