Properties

Base field \(\Q(\sqrt{-3}) \)
Label 2.0.3.1-129792.2-h
Conductor 129792.2
Rank \( 1 \)

Related objects

Learn more

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

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

Elliptic curves in class 129792.2-h over \(\Q(\sqrt{-3}) \)

Isogeny class 129792.2-h contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
129792.2-h1 \( \bigl[0\) , \( -1\) , \( 0\) , \( 8\) , \( 448\bigr] \)
129792.2-h2 \( \bigl[0\) , \( -1\) , \( 0\) , \( -7\) , \( -2\bigr] \)
129792.2-h3 \( \bigl[0\) , \( -1\) , \( 0\) , \( -52\) , \( 160\bigr] \)
129792.2-h4 \( \bigl[0\) , \( -1\) , \( 0\) , \( -880 a + 928\) , \( 1152 a + 9568\bigr] \)
129792.2-h5 \( \bigl[0\) , \( -1\) , \( 0\) , \( 880 a + 48\) , \( -1152 a + 10720\bigr] \)
129792.2-h6 \( \bigl[0\) , \( -1\) , \( 0\) , \( -832\) , \( 9520\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 4 & 2 & 2 & 2 & 4 \\ 4 & 1 & 2 & 8 & 8 & 4 \\ 2 & 2 & 1 & 4 & 4 & 2 \\ 2 & 8 & 4 & 1 & 4 & 8 \\ 2 & 8 & 4 & 4 & 1 & 8 \\ 4 & 4 & 2 & 8 & 8 & 1 \end{array}\right)\)

Isogeny graph