Properties

Base field \(\Q(\sqrt{-2}) \)
Label 2.0.8.1-392.1-a
Conductor 392.1
Rank \( 1 \)

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

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

Elliptic curves in class 392.1-a over \(\Q(\sqrt{-2}) \)

Isogeny class 392.1-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
392.1-a1 \( \bigl[a\) , \( -1\) , \( a\) , \( 2\) , \( 0\bigr] \)
392.1-a2 \( \bigl[a\) , \( -1\) , \( a\) , \( -13\) , \( 25\bigr] \)
392.1-a3 \( \bigl[a\) , \( -1\) , \( a\) , \( -3\) , \( -1\bigr] \)
392.1-a4 \( \bigl[a\) , \( -1\) , \( a\) , \( -73\) , \( -211\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph