Properties

Base field \(\Q(\sqrt{-3}) \)
Label 2.0.3.1-33124.5-a
Conductor 33124.5
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 33124.5-a over \(\Q(\sqrt{-3}) \)

Isogeny class 33124.5-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
33124.5-a1 \( \bigl[a\) , \( -a + 1\) , \( 1\) , \( -867 a\) , \( 6445\bigr] \)
33124.5-a2 \( \bigl[a\) , \( -a + 1\) , \( 1\) , \( 4253 a\) , \( 59693\bigr] \)
33124.5-a3 \( \bigl[a\) , \( -a + 1\) , \( 1\) , \( 31293 a\) , \( -2081875\bigr] \)
33124.5-a4 \( \bigl[a\) , \( -a + 1\) , \( 1\) , \( 59133 a\) , \( 5547693\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph