Elliptic curve isogeny class 6498.5-b over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-6498.5-b
• Conductor: 6498.5
• Rank: \( 0 \)

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

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

Elliptic curves in class 6498.5-b over \(\Q(\sqrt{-2}) \)

Isogeny class 6498.5-b contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
6498.5-b1	\( \bigl[1\) , \( 1\) , \( 1\) , \( -5312\) , \( -167551\bigr] \)
6498.5-b2	\( \bigl[1\) , \( 1\) , \( 1\) , \( 10220 a - 4032\) , \( -590688 a - 472255\bigr] \)
6498.5-b3	\( \bigl[1\) , \( 1\) , \( 1\) , \( -10220 a - 4032\) , \( 590688 a - 472255\bigr] \)
6498.5-b4	\( \bigl[1\) , \( 1\) , \( 1\) , \( -352\) , \( -2431\bigr] \)
6498.5-b5	\( \bigl[1\) , \( 1\) , \( 1\) , \( -5472\) , \( -158079\bigr] \)
6498.5-b6	\( \bigl[1\) , \( 1\) , \( 1\) , \( -87552\) , \( -10007679\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph