Elliptic curve isogeny class 41616.4-d over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-41616.4-d
• Conductor: 41616.4
• Rank: \( 0 \)

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

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

Elliptic curves in class 41616.4-d over \(\Q(\sqrt{-2}) \)

Isogeny class 41616.4-d contains 4 curves linked by isogenies of degrees dividing 10.

Curve label	Weierstrass Coefficients
41616.4-d1	\( \bigl[a\) , \( a - 1\) , \( 0\) , \( -23093 a - 2242\) , \( 1094982 a - 3495813\bigr] \)
41616.4-d2	\( \bigl[a\) , \( a - 1\) , \( 0\) , \( 347 a - 342\) , \( 3226 a - 317\bigr] \)
41616.4-d3	\( \bigl[a\) , \( a - 1\) , \( 0\) , \( 1247 a - 1862\) , \( -29870 a + 21515\bigr] \)
41616.4-d4	\( \bigl[a\) , \( a - 1\) , \( 0\) , \( -26693 a + 3838\) , \( 1206310 a - 2275877\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 10 & 5 & 2 \\ 10 & 1 & 2 & 5 \\ 5 & 2 & 1 & 10 \\ 2 & 5 & 10 & 1 \end{array}\right)\)

Isogeny graph