Elliptic curve isogeny class 16200.3-g over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-16200.3-g
• Conductor: 16200.3
• Rank: \( 0 \)

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

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

Elliptic curves in class 16200.3-g over \(\Q(\sqrt{-2}) \)

Isogeny class 16200.3-g contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
16200.3-g1	\( \bigl[a\) , \( -1\) , \( a\) , \( -179\) , \( -7919\bigr] \)
16200.3-g2	\( \bigl[a\) , \( -1\) , \( a\) , \( 181\) , \( 91\bigr] \)
16200.3-g3	\( \bigl[a\) , \( -1\) , \( a\) , \( -44\) , \( 46\bigr] \)
16200.3-g4	\( \bigl[a\) , \( -1\) , \( a\) , \( -449\) , \( -3437\bigr] \)
16200.3-g5	\( \bigl[0\) , \( 0\) , \( 0\) , \( -138\) , \( -623\bigr] \)
16200.3-g6	\( \bigl[a\) , \( -1\) , \( a\) , \( -7199\) , \( -231587\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph