Elliptic curve isogeny class 41616.5-e over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-41616.5-e
• Conductor: 41616.5
• Rank: \( 1 \)

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

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

Elliptic curves in class 41616.5-e over \(\Q(\sqrt{-2}) \)

Isogeny class 41616.5-e contains 8 curves linked by isogenies of degrees dividing 12.

Curve label	Weierstrass Coefficients
41616.5-e1	\( \bigl[a\) , \( 1\) , \( 0\) , \( -34240 a + 89158\) , \( -6490880 a - 8469742\bigr] \)
41616.5-e2	\( \bigl[a\) , \( 1\) , \( 0\) , \( 34240 a + 89158\) , \( 6490880 a - 8469742\bigr] \)
41616.5-e3	\( \bigl[a\) , \( 1\) , \( 0\) , \( -4360 a + 418\) , \( -97280 a + 146930\bigr] \)
41616.5-e4	\( \bigl[a\) , \( 1\) , \( 0\) , \( 4360 a + 418\) , \( 97280 a + 146930\bigr] \)
41616.5-e5	\( \bigl[a\) , \( 1\) , \( 0\) , \( -862\) , \( 16498\bigr] \)
41616.5-e6	\( \bigl[a\) , \( 1\) , \( 0\) , \( 7238\) , \( -302318\bigr] \)
41616.5-e7	\( \bigl[a\) , \( 1\) , \( 0\) , \( -3002\) , \( -48366\bigr] \)
41616.5-e8	\( \bigl[a\) , \( 1\) , \( 0\) , \( -1022\) , \( 12402\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 4 & 3 & 12 & 6 & 2 & 4 & 12 \\ 4 & 1 & 12 & 3 & 6 & 2 & 4 & 12 \\ 3 & 12 & 1 & 4 & 2 & 6 & 12 & 4 \\ 12 & 3 & 4 & 1 & 2 & 6 & 12 & 4 \\ 6 & 6 & 2 & 2 & 1 & 3 & 6 & 2 \\ 2 & 2 & 6 & 6 & 3 & 1 & 2 & 6 \\ 4 & 4 & 12 & 12 & 6 & 2 & 1 & 3 \\ 12 & 12 & 4 & 4 & 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph