Properties

Base field \(\Q(\sqrt{-3}) \)
Label 2.0.3.1-8379.1-a
Conductor 8379.1
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 8379.1-a over \(\Q(\sqrt{-3}) \)

Isogeny class 8379.1-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label Weierstrass Coefficients
8379.1-a1 \( \bigl[1\) , \( a\) , \( a + 1\) , \( -17 a + 19\) , \( 11 a + 34\bigr] \)
8379.1-a2 \( \bigl[1\) , \( a\) , \( a + 1\) , \( 48 a + 9\) , \( -72 a + 239\bigr] \)
8379.1-a3 \( \bigl[a + 1\) , \( 0\) , \( 1\) , \( -17 a + 4\) , \( 9 a + 1\bigr] \)
8379.1-a4 \( \bigl[a + 1\) , \( 0\) , \( 1\) , \( -212 a + 34\) , \( 1149 a - 785\bigr] \)

Rank

Rank: \( 1 \)

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