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

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-41616.5-n
• Conductor: 41616.5
• Rank: \( 0 \)

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

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

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

Isogeny class 41616.5-n contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
41616.5-n1	\( \bigl[a\) , \( -a - 1\) , \( a\) , \( 4350 a + 369\) , \( -86669 a - 140167\bigr] \)
41616.5-n2	\( \bigl[a\) , \( -a - 1\) , \( a\) , \( 270 a + 29\) , \( -1533 a - 2059\bigr] \)
41616.5-n3	\( \bigl[a\) , \( -a - 1\) , \( a\) , \( 30 a - 631\) , \( -45 a - 12655\bigr] \)
41616.5-n4	\( \bigl[a\) , \( -a - 1\) , \( a\) , \( 30 a + 49\) , \( -141 a + 137\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph