Properties

Base field \(\Q(\sqrt{-3}) \)
Label 2.0.3.1-85692.2-a
Conductor 85692.2
Rank \( 2 \)

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 85692.2-a over \(\Q(\sqrt{-3}) \)

Isogeny class 85692.2-a contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
85692.2-a1 \( \bigl[a + 1\) , \( -a + 1\) , \( 1\) , \( -10 a + 7\) , \( -3 a + 9\bigr] \)
85692.2-a2 \( \bigl[a + 1\) , \( -a + 1\) , \( 1\) , \( 30 a - 13\) , \( -3 a + 57\bigr] \)

Rank

Rank: \( 2 \)

Isogeny matrix

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

Isogeny graph