Properties

Base field \(\Q(\sqrt{-3}) \)
Label 2.0.3.1-8379.2-d
Conductor 8379.2
Rank \( 0 \)

Related objects

Learn more about

Base field \(\Q(\sqrt{-3}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x + 1 \); class number \(1\).

Elliptic curves in class 8379.2-d over \(\Q(\sqrt{-3}) \)

Isogeny class 8379.2-d contains 4 curves linked by isogenies of degrees dividing 6.

Curve label Weierstrass Coefficients
8379.2-d1 \( \bigl[1\) , \( a\) , \( a\) , \( -20 a + 3\) , \( -47 a + 31\bigr] \)
8379.2-d2 \( \bigl[1\) , \( a\) , \( a\) , \( 35 a - 62\) , \( -184 a + 233\bigr] \)
8379.2-d3 \( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -15\) , \( -12 a - 4\bigr] \)
8379.2-d4 \( \bigl[a + 1\) , \( 0\) , \( 0\) , \( -30 a - 180\) , \( -297 a - 910\bigr] \)

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