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

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-6498.5-a
• Conductor: 6498.5
• Rank: \( 1 \)

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

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

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

Isogeny class 6498.5-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
6498.5-a1	\( \bigl[1\) , \( 1\) , \( 0\) , \( -335 a - 5\) , \( 2255 a - 2941\bigr] \)
6498.5-a2	\( \bigl[1\) , \( 1\) , \( 0\) , \( 335 a - 5\) , \( -2255 a - 2941\bigr] \)
6498.5-a3	\( \bigl[1\) , \( 1\) , \( 0\) , \( -85\) , \( -473\bigr] \)
6498.5-a4	\( \bigl[1\) , \( 1\) , \( 0\) , \( -95\) , \( -399\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph