Properties

Base field \(\Q(\sqrt{-3}) \)
Label 2.0.3.1-3249.1-a
Conductor 3249.1
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 3249.1-a over \(\Q(\sqrt{-3}) \)

Isogeny class 3249.1-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label Weierstrass Coefficients
3249.1-a1 \( \bigl[1\) , \( a\) , \( 1\) , \( -17 a + 56\) , \( -156 a + 42\bigr] \)
3249.1-a2 \( \bigl[1\) , \( a\) , \( 1\) , \( 168 a - 74\) , \( -544 a - 622\bigr] \)
3249.1-a3 \( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -45 a + 36\) , \( -48 a + 62\bigr] \)
3249.1-a4 \( \bigl[a + 1\) , \( 0\) , \( a + 1\) , \( -600 a + 426\) , \( -2310 a + 5603\bigr] \)

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