Properties

Base field \(\Q(\sqrt{-2}) \)
Label 2.0.8.1-258.4-a
Conductor 258.4
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 258.4-a over \(\Q(\sqrt{-2}) \)

Isogeny class 258.4-a contains 2 curves linked by isogenies of degree 2.

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

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph