Properties

Base field \(\Q(\sqrt{-2}) \)
Label 2.0.8.1-23409.8-i
Conductor 23409.8
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 23409.8-i over \(\Q(\sqrt{-2}) \)

Isogeny class 23409.8-i contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
23409.8-i1 \( \bigl[1\) , \( -1\) , \( 0\) , \( -6\) , \( 377\bigr] \)
23409.8-i2 \( \bigl[1\) , \( -1\) , \( 0\) , \( -6\) , \( -1\bigr] \)
23409.8-i3 \( \bigl[1\) , \( -1\) , \( 0\) , \( -51\) , \( 152\bigr] \)
23409.8-i4 \( \bigl[1\) , \( -1\) , \( 0\) , \( -816\) , \( 9179\bigr] \)

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