Properties

Base field \(\Q(\sqrt{-2}) \)
Label 2.0.8.1-225.3-a
Conductor 225.3
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 225.3-a over \(\Q(\sqrt{-2}) \)

Isogeny class 225.3-a contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
225.3-a1 \( \bigl[a\) , \( -1\) , \( 1\) , \( 2 a + 8\) , \( 4 a - 9\bigr] \)
225.3-a2 \( \bigl[a\) , \( -1\) , \( a + 1\) , \( -3 a + 2\) , \( -a + 5\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph