Properties

Base field \(\Q(\sqrt{-3}) \)
Label 2.0.3.1-54684.2-a
Conductor 54684.2
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 54684.2-a over \(\Q(\sqrt{-3}) \)

Isogeny class 54684.2-a contains 5 curves linked by isogenies of degrees dividing 9.

Curve label Weierstrass Coefficients
54684.2-a1 \( \bigl[1\) , \( a\) , \( 0\) , \( -367 a + 554\) , \( 2293 a + 3767\bigr] \)
54684.2-a2 \( \bigl[1\) , \( a\) , \( 0\) , \( 3053 a - 4156\) , \( 6565 a - 58879\bigr] \)
54684.2-a3 \( \bigl[1\) , \( a\) , \( 0\) , \( 83 a + 89\) , \( -527 a + 752\bigr] \)
54684.2-a4 \( \bigl[1\) , \( a\) , \( 0\) , \( -7717 a - 3856\) , \( 397303 a - 10303\bigr] \)
54684.2-a5 \( \bigl[1\) , \( a\) , \( 0\) , \( -32887 a + 47339\) , \( 1679851 a + 2156108\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrr} 1 & 3 & 3 & 3 & 3 \\ 3 & 1 & 9 & 9 & 9 \\ 3 & 9 & 1 & 9 & 9 \\ 3 & 9 & 9 & 1 & 9 \\ 3 & 9 & 9 & 9 & 1 \end{array}\right)\)

Isogeny graph