Properties

Base field \(\Q(\sqrt{-3}) \)
Label 2.0.3.1-228.2-a
Conductor 228.2
Rank \( 0 \)

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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 228.2-a over \(\Q(\sqrt{-3}) \)

Isogeny class 228.2-a contains 4 curves linked by isogenies of degrees dividing 10.

Curve label Weierstrass Coefficients
228.2-a1 \( \bigl[1\) , \( -a - 1\) , \( 1\) , \( -140 a + 35\) , \( -615 a + 881\bigr] \)
228.2-a2 \( \bigl[1\) , \( -a - 1\) , \( 1\) , \( 0\) , \( a - 1\bigr] \)
228.2-a3 \( \bigl[1\) , \( -a - 1\) , \( 1\) , \( 20 a + 35\) , \( -167 a + 113\bigr] \)
228.2-a4 \( \bigl[1\) , \( -a - 1\) , \( 1\) , \( 10 a - 10\) , \( 9 a - 1\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 10 & 2 & 5 \\ 10 & 1 & 5 & 2 \\ 2 & 5 & 1 & 10 \\ 5 & 2 & 10 & 1 \end{array}\right)\)

Isogeny graph