Properties

Base field \(\Q(\sqrt{-3}) \)
Label 2.0.3.1-147456.1-f
Conductor 147456.1
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 147456.1-f over \(\Q(\sqrt{-3}) \)

Isogeny class 147456.1-f contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
147456.1-f1 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -23 a + 16\) , \( -14 a + 63\bigr] \)
147456.1-f2 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 7 a + 1\) , \( a + 6\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph