Properties

Base field \(\Q(\sqrt{-3}) \)
Label 2.0.3.1-13689.1-CMb
Conductor 13689.1
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 13689.1-CMb over \(\Q(\sqrt{-3}) \)

Isogeny class 13689.1-CMb contains 2 curves linked by isogenies of degree 3.

Curve label Weierstrass Coefficients
13689.1-CMb1 \( \bigl[0\) , \( 0\) , \( 1\) , \( 0\) , \( 9 a + 4\bigr] \)
13689.1-CMb2 \( \bigl[0\) , \( 0\) , \( 1\) , \( -210 a - 240\) , \( 2277 a + 1075\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph