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

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-34848.5-d
• Conductor: 34848.5
• Rank: \( 1 \)

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

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

Rank

Rank: \( 1 \)

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

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

Isogeny class 34848.5-d contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
34848.5-d1	\( \bigl[a\) , \( 1\) , \( a\) , \( 1\) , \( -4\bigr] \)
34848.5-d2	\( \bigl[a\) , \( 1\) , \( a\) , \( -25 a + 21\) , \( -3 a - 94\bigr] \)
34848.5-d3	\( \bigl[a\) , \( 1\) , \( a\) , \( 25 a + 21\) , \( 3 a - 94\bigr] \)
34848.5-d4	\( \bigl[0\) , \( -1\) , \( 0\) , \( -10\) , \( 16\bigr] \)