Properties

Base field \(\Q(\sqrt{-3}) \)
Label 2.0.3.1-28899.6-d
Conductor 28899.6
Rank \( 1 \)

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 28899.6-d over \(\Q(\sqrt{-3}) \)

Isogeny class 28899.6-d contains 4 curves linked by isogenies of degrees dividing 6.

Curve label Weierstrass Coefficients
28899.6-d1 \( \bigl[a\) , \( -a + 1\) , \( 1\) , \( 123 a - 4\) , \( 27 a + 533\bigr] \)
28899.6-d2 \( \bigl[a\) , \( -a + 1\) , \( 1\) , \( 223 a - 339\) , \( -2607 a + 3087\bigr] \)
28899.6-d3 \( \bigl[a\) , \( -a + 1\) , \( 1\) , \( -107 a + 6\) , \( -525 a + 219\bigr] \)
28899.6-d4 \( \bigl[a\) , \( -a + 1\) , \( 1\) , \( 8 a + 1\) , \( 3 a + 5\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph