Properties

Base field \(\Q(\sqrt{-2}) \)
Label 2.0.8.1-41616.1-f
Conductor 41616.1
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 41616.1-f over \(\Q(\sqrt{-2}) \)

Isogeny class 41616.1-f contains 2 curves linked by isogenies of degree 3.

Curve label Weierstrass Coefficients
41616.1-f1 \( \bigl[a\) , \( a\) , \( 0\) , \( 222 a - 276\) , \( -1824 a + 572\bigr] \)
41616.1-f2 \( \bigl[a\) , \( a\) , \( a\) , \( 315 a + 223\) , \( 492 a + 3703\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph