Elliptic curve isogeny class 43218.2-f over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-43218.2-f
• Conductor: 43218.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 43218.2-f over \(\Q(\sqrt{-2}) \)

Isogeny class 43218.2-f contains 8 curves linked by isogenies of degrees dividing 16.

Curve label	Weierstrass Coefficients
43218.2-f1	\( \bigl[1\) , \( 0\) , \( 0\) , \( -197\) , \( -2367\bigr] \)
43218.2-f2	\( \bigl[1\) , \( 0\) , \( 0\) , \( 18913\) , \( -381333\bigr] \)
43218.2-f3	\( \bigl[1\) , \( 0\) , \( 0\) , \( -5097\) , \( -49995\bigr] \)
43218.2-f4	\( \bigl[1\) , \( 0\) , \( 0\) , \( -44787\) , \( 3609423\bigr] \)
43218.2-f5	\( \bigl[1\) , \( 0\) , \( 0\) , \( -29155 a + 210993\) , \( -25951037 a - 11032169\bigr] \)
43218.2-f6	\( \bigl[1\) , \( 0\) , \( 0\) , \( 29155 a + 210993\) , \( 25951037 a - 11032169\bigr] \)
43218.2-f7	\( \bigl[1\) , \( 0\) , \( 0\) , \( -4117\) , \( -101935\bigr] \)
43218.2-f8	\( \bigl[1\) , \( 0\) , \( 0\) , \( -65857\) , \( -6510547\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph