Properties

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

Isogeny class 41616.5-p contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
41616.5-p1 \( \bigl[0\) , \( -a\) , \( 0\) , \( 22 a + 62\) , \( 102 a - 129\bigr] \)
41616.5-p2 \( \bigl[a\) , \( -a - 1\) , \( a\) , \( -51 a + 143\) , \( 396 a + 422\bigr] \)
41616.5-p3 \( \bigl[a\) , \( -a - 1\) , \( a\) , \( 4 a + 18\) , \( -18 a + 23\bigr] \)
41616.5-p4 \( \bigl[a\) , \( -a - 1\) , \( a\) , \( 19 a - 87\) , \( -120 a + 278\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph