Properties

Base field \(\Q(\sqrt{-2}) \)
Label 2.0.8.1-13689.3-a
Conductor 13689.3
Rank \( 2 \)

Related objects

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Base field \(\Q(\sqrt{-2}) \)

Generator \(a\), with minimal polynomial \( x^{2} + 2 \); class number \(1\).

Elliptic curves in class 13689.3-a over \(\Q(\sqrt{-2}) \)

Isogeny class 13689.3-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
13689.3-a1 \( \bigl[1\) , \( -1\) , \( 1\) , \( 4\) , \( 6\bigr] \)
13689.3-a2 \( \bigl[1\) , \( -1\) , \( 1\) , \( -41\) , \( 96\bigr] \)
13689.3-a3 \( \bigl[1\) , \( -1\) , \( 1\) , \( -176\) , \( -768\bigr] \)
13689.3-a4 \( \bigl[1\) , \( -1\) , \( 1\) , \( -626\) , \( 6180\bigr] \)

Rank

Rank: \( 2 \)

Isogeny matrix

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

Isogeny graph