Elliptic curve isogeny class 34848.5-e over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-34848.5-e
• Conductor: 34848.5
• Rank: \( 0 \)

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

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

Elliptic curves in class 34848.5-e over \(\Q(\sqrt{-2}) \)

Isogeny class 34848.5-e contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
34848.5-e1	\( \bigl[a\) , \( 1\) , \( a\) , \( 105 a + 195\) , \( -567 a + 1254\bigr] \)
34848.5-e2	\( \bigl[a\) , \( 1\) , \( a\) , \( -105 a + 195\) , \( 567 a + 1254\bigr] \)
34848.5-e3	\( \bigl[a\) , \( 1\) , \( a\) , \( 15\) , \( 48\bigr] \)
34848.5-e4	\( \bigl[0\) , \( -1\) , \( 0\) , \( -34\) , \( -56\bigr] \)
34848.5-e5	\( \bigl[a\) , \( 1\) , \( 0\) , \( -36\) , \( -81\bigr] \)
34848.5-e6	\( \bigl[0\) , \( -1\) , \( 0\) , \( -132\) , \( 630\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph