Properties

Base field \(\Q(\sqrt{-3}) \)
Label 2.0.3.1-28224.2-g
Conductor 28224.2
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 28224.2-g over \(\Q(\sqrt{-3}) \)

Isogeny class 28224.2-g contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
28224.2-g1 \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 18 a - 21\) , \( -45 a + 45\bigr] \)
28224.2-g2 \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -282 a + 339\) , \( -441 a - 2331\bigr] \)
28224.2-g3 \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -42 a - 21\) , \( -201 a - 3\bigr] \)
28224.2-g4 \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -762 a - 381\) , \( -11865 a + 213\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph