Properties

Base field \(\Q(\sqrt{-2}) \)
Label 2.0.8.1-5776.2-c
Conductor 5776.2
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 5776.2-c over \(\Q(\sqrt{-2}) \)

Isogeny class 5776.2-c contains 3 curves linked by isogenies of degrees dividing 9.

Curve label Weierstrass Coefficients
5776.2-c1 \( \bigl[a\) , \( 1\) , \( 0\) , \( -62\) , \( 178\bigr] \)
5776.2-c2 \( \bigl[a\) , \( 1\) , \( 0\) , \( -342\) , \( -19646\bigr] \)
5776.2-c3 \( \bigl[a\) , \( 1\) , \( 0\) , \( 38\) , \( 722\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph