Properties

Base field \(\Q(\sqrt{-2}) \)
Label 2.0.8.1-41616.5-i
Conductor 41616.5
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 41616.5-i over \(\Q(\sqrt{-2}) \)

Isogeny class 41616.5-i contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
41616.5-i1 \( \bigl[a\) , \( a - 1\) , \( 0\) , \( -361 a - 544\) , \( 3708 a + 2421\bigr] \)
41616.5-i2 \( \bigl[a\) , \( a - 1\) , \( 0\) , \( -121 a - 224\) , \( -1028 a - 811\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph