Properties

Base field \(\Q(\sqrt{-3}) \)
Label 2.0.3.1-3249.3-a
Conductor 3249.3
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 3249.3-a over \(\Q(\sqrt{-3}) \)

Isogeny class 3249.3-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label Weierstrass Coefficients
3249.3-a1 \( \bigl[1\) , \( -a + 1\) , \( 1\) , \( 17 a + 39\) , \( 156 a - 114\bigr] \)
3249.3-a2 \( \bigl[1\) , \( -a + 1\) , \( 1\) , \( -168 a + 94\) , \( 544 a - 1166\bigr] \)
3249.3-a3 \( \bigl[a + 1\) , \( 0\) , \( a\) , \( -37 a + 44\) , \( 47 a + 15\bigr] \)
3249.3-a4 \( \bigl[a + 1\) , \( 0\) , \( a\) , \( -427 a + 599\) , \( 2309 a + 3294\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph