Properties

Base field \(\Q(\sqrt{-2}) \)
Label 2.0.8.1-5625.2-c
Conductor 5625.2
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 5625.2-c over \(\Q(\sqrt{-2}) \)

Isogeny class 5625.2-c contains 2 curves linked by isogenies of degree 5.

Curve label Weierstrass Coefficients
5625.2-c1 \( \bigl[0\) , \( -1\) , \( 1\) , \( -8\) , \( -7\bigr] \)
5625.2-c2 \( \bigl[0\) , \( -1\) , \( 1\) , \( 42\) , \( 443\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph