Properties

Base field \(\Q(\sqrt{-3}) \)
Label 2.0.3.1-523.1-a
Conductor 523.1
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 523.1-a over \(\Q(\sqrt{-3}) \)

Isogeny class 523.1-a contains 2 curves linked by isogenies of degree 3.

Curve label Weierstrass Coefficients
523.1-a1 \( \bigl[1\) , \( -a - 1\) , \( 1\) , \( 18 a - 22\) , \( -40 a + 39\bigr] \)
523.1-a2 \( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( -2 a - 2\) , \( 1\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph