Properties

Base field \(\Q(\sqrt{-2}) \)
Label 2.0.8.1-36864.2-o
Conductor 36864.2
Rank \( 0 \)

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 36864.2-o over \(\Q(\sqrt{-2}) \)

Isogeny class 36864.2-o contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
36864.2-o1 \( \bigl[0\) , \( 1\) , \( 0\) , \( -a\) , \( a - 2\bigr] \)
36864.2-o2 \( \bigl[0\) , \( 1\) , \( 0\) , \( a - 6\) , \( -a + 4\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph