Properties

Base field \(\Q(\sqrt{-2}) \)
Label 2.0.8.1-297.2-a
Conductor 297.2
Rank \( 0 \)

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 297.2-a over \(\Q(\sqrt{-2}) \)

Isogeny class 297.2-a contains 3 curves linked by isogenies of degrees dividing 9.

Curve label Weierstrass Coefficients
297.2-a1 \( \bigl[0\) , \( -a - 1\) , \( 1\) , \( 11 a + 11\) , \( -3 a - 27\bigr] \)
297.2-a2 \( \bigl[0\) , \( -a - 1\) , \( 1\) , \( -39 a - 9\) , \( 39 a - 210\bigr] \)
297.2-a3 \( \bigl[0\) , \( -a - 1\) , \( 1\) , \( a + 1\) , \( -a\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph