Properties

Base field \(\Q(\sqrt{-2}) \)
Label 2.0.8.1-34848.9-g
Conductor 34848.9
Rank \( 0 \)

Related objects

Learn more

Base field \(\Q(\sqrt{-2}) \)

Generator \(a\), with minimal polynomial \( x^{2} + 2 \); class number \(1\).

Elliptic curves in class 34848.9-g over \(\Q(\sqrt{-2}) \)

Isogeny class 34848.9-g contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
34848.9-g1 \( \bigl[0\) , \( 0\) , \( 0\) , \( 8 a + 31\) , \( 0\bigr] \)
34848.9-g2 \( \bigl[0\) , \( 0\) , \( 0\) , \( -8 a - 31\) , \( 0\bigr] \)
34848.9-g3 \( \bigl[a\) , \( -1\) , \( 0\) , \( 22 a + 86\) , \( 192 a - 209\bigr] \)
34848.9-g4 \( \bigl[a\) , \( -1\) , \( a\) , \( 22 a + 87\) , \( -214 a + 124\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph