Properties

Base field \(\Q(\sqrt{-2}) \)
Label 2.0.8.1-32400.3-h
Conductor 32400.3
Rank \( 1 \)

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 32400.3-h over \(\Q(\sqrt{-2}) \)

Isogeny class 32400.3-h contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
32400.3-h1 \( \bigl[a\) , \( -1\) , \( 0\) , \( 9\) , \( 0\bigr] \)
32400.3-h2 \( \bigl[a\) , \( -1\) , \( 0\) , \( -36\) , \( 54\bigr] \)
32400.3-h3 \( \bigl[a\) , \( -1\) , \( 0\) , \( -306\) , \( -1890\bigr] \)
32400.3-h4 \( \bigl[a\) , \( -1\) , \( 0\) , \( -486\) , \( 4374\bigr] \)

Rank

Rank: \( 1 \)

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