Properties

Base field \(\Q(\sqrt{-2}) \)
Label 2.0.8.1-29241.8-b
Conductor 29241.8
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 29241.8-b over \(\Q(\sqrt{-2}) \)

Isogeny class 29241.8-b contains 3 curves linked by isogenies of degrees dividing 9.

Curve label Weierstrass Coefficients
29241.8-b1 \( \bigl[0\) , \( 0\) , \( 1\) , \( -6924\) , \( 221760\bigr] \)
29241.8-b2 \( \bigl[0\) , \( 0\) , \( 1\) , \( -84\) , \( 315\bigr] \)
29241.8-b3 \( \bigl[0\) , \( 0\) , \( 1\) , \( 6\) , \( 0\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph