Elliptic curve isogeny class 45000.2-i over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-45000.2-i
• Conductor: 45000.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 45000.2-i over \(\Q(\sqrt{-2}) \)

Isogeny class 45000.2-i contains 8 curves linked by isogenies of degrees dividing 16.

Curve label	Weierstrass Coefficients
45000.2-i1	\( \bigl[a\) , \( 0\) , \( 0\) , \( 98\) , \( 2714\bigr] \)
45000.2-i2	\( \bigl[0\) , \( 1\) , \( 0\) , \( 17\) , \( 38\bigr] \)
45000.2-i3	\( \bigl[a\) , \( 0\) , \( 0\) , \( -27\) , \( -36\bigr] \)
45000.2-i4	\( \bigl[a\) , \( 0\) , \( 0\) , \( -152\) , \( 714\bigr] \)
45000.2-i5	\( \bigl[a\) , \( 0\) , \( 0\) , \( 1750 a + 2098\) , \( -14000 a + 67714\bigr] \)
45000.2-i6	\( \bigl[a\) , \( 0\) , \( 0\) , \( -1750 a + 2098\) , \( 14000 a + 67714\bigr] \)
45000.2-i7	\( \bigl[a\) , \( 0\) , \( 0\) , \( -402\) , \( -3036\bigr] \)
45000.2-i8	\( \bigl[a\) , \( 0\) , \( 0\) , \( -2402\) , \( 45714\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 8 & 4 & 2 & 2 & 2 & 8 & 4 \\ 8 & 1 & 2 & 4 & 16 & 16 & 4 & 8 \\ 4 & 2 & 1 & 2 & 8 & 8 & 2 & 4 \\ 2 & 4 & 2 & 1 & 4 & 4 & 4 & 2 \\ 2 & 16 & 8 & 4 & 1 & 4 & 16 & 8 \\ 2 & 16 & 8 & 4 & 4 & 1 & 16 & 8 \\ 8 & 4 & 2 & 4 & 16 & 16 & 1 & 8 \\ 4 & 8 & 4 & 2 & 8 & 8 & 8 & 1 \end{array}\right)\)

Isogeny graph