Properties

Base field \(\Q(\sqrt{-2}) \)
Label 2.0.8.1-20808.5-h
Conductor 20808.5
Rank \( 0 \)

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 20808.5-h over \(\Q(\sqrt{-2}) \)

Isogeny class 20808.5-h contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
20808.5-h1 \( \bigl[a\) , \( 0\) , \( 0\) , \( 72\) , \( -36\bigr] \)
20808.5-h2 \( \bigl[a\) , \( 0\) , \( 0\) , \( -18\) , \( 0\bigr] \)
20808.5-h3 \( \bigl[a\) , \( 0\) , \( 0\) , \( -188\) , \( 1020\bigr] \)
20808.5-h4 \( \bigl[a\) , \( 0\) , \( 0\) , \( -30 a + 792\) , \( -6036 a - 828\bigr] \)
20808.5-h5 \( \bigl[a\) , \( 0\) , \( 0\) , \( 30 a + 792\) , \( 6036 a - 828\bigr] \)
20808.5-h6 \( \bigl[a\) , \( 0\) , \( 0\) , \( -13\) , \( -16\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 2 & 2 & 4 \\ 2 & 1 & 2 & 4 & 4 & 2 \\ 4 & 2 & 1 & 8 & 8 & 4 \\ 2 & 4 & 8 & 1 & 4 & 8 \\ 2 & 4 & 8 & 4 & 1 & 8 \\ 4 & 2 & 4 & 8 & 8 & 1 \end{array}\right)\)

Isogeny graph