Properties

Base field \(\Q(\sqrt{-2}) \)
Label 2.0.8.1-2592.3-d
Conductor 2592.3
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 2592.3-d over \(\Q(\sqrt{-2}) \)

Isogeny class 2592.3-d contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
2592.3-d1 \( \bigl[0\) , \( 0\) , \( 0\) , \( 9\) , \( 0\bigr] \)
2592.3-d2 \( \bigl[0\) , \( 0\) , \( 0\) , \( -9\) , \( 0\bigr] \)
2592.3-d3 \( \bigl[a\) , \( -1\) , \( 0\) , \( -24\) , \( -35\bigr] \)
2592.3-d4 \( \bigl[a\) , \( -1\) , \( a\) , \( -23\) , \( 60\bigr] \)

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