Properties

Base field \(\Q(\sqrt{-3}) \)
Label 2.0.3.1-134199.7-a
Conductor 134199.7
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 134199.7-a over \(\Q(\sqrt{-3}) \)

Isogeny class 134199.7-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
134199.7-a1 \( \bigl[1\) , \( a\) , \( a + 1\) , \( -55 a + 26\) , \( 91 a - 120\bigr] \)
134199.7-a2 \( \bigl[1\) , \( a\) , \( a + 1\) , \( -385 a + 626\) , \( 3265 a + 2700\bigr] \)
134199.7-a3 \( \bigl[1\) , \( a\) , \( a + 1\) , \( -55 a + 41\) , \( 166 a - 96\bigr] \)
134199.7-a4 \( \bigl[1\) , \( a\) , \( a + 1\) , \( 275 a - 304\) , \( 1627 a - 1416\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph