Properties

Base field \(\Q(\sqrt{-3}) \)
Label 2.0.3.1-18688.1-e
Conductor 18688.1
Rank not recorded

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 18688.1-e over \(\Q(\sqrt{-3}) \)

Isogeny class 18688.1-e contains 4 curves linked by isogenies of degrees dividing 6.

Curve label Weierstrass Coefficients
18688.1-e1 \( \bigl[0\) , \( a\) , \( 0\) , \( -234 a + 77\) , \( 1113 a - 1050\bigr] \)
18688.1-e2 \( \bigl[0\) , \( a\) , \( 0\) , \( 86 a - 83\) , \( 345 a - 186\bigr] \)
18688.1-e3 \( \bigl[0\) , \( a\) , \( 0\) , \( 6 a - 3\) , \( 9 a - 10\bigr] \)
18688.1-e4 \( \bigl[0\) , \( a\) , \( 0\) , \( -234 a + 157\) , \( 1849 a - 714\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

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

Isogeny graph