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

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-41616.4-i
• Conductor: 41616.4
• Rank: \( 1 \)

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

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

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

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

Curve label	Weierstrass Coefficients
41616.4-i1	\( \bigl[a\) , \( 0\) , \( 0\) , \( -173 a + 1910\) , \( -37068 a + 15081\bigr] \)
41616.4-i2	\( \bigl[a\) , \( 0\) , \( 0\) , \( -13 a - 30\) , \( -32 a - 47\bigr] \)
41616.4-i3	\( \bigl[a\) , \( 0\) , \( 0\) , \( -73 a - 110\) , \( 440 a + 265\bigr] \)
41616.4-i4	\( \bigl[a\) , \( 0\) , \( 0\) , \( 67 a + 2230\) , \( -28652 a + 2185\bigr] \)

Rank

Rank: \( 1 \)

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