Elliptic curve isogeny class 8450.1-a over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-8450.1-a
• Conductor: 8450.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 8450.1-a over \(\Q(\sqrt{-2}) \)

Isogeny class 8450.1-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
8450.1-a1	\( \bigl[1\) , \( 0\) , \( 1\) , \( -13\) , \( 156\bigr] \)
8450.1-a2	\( \bigl[1\) , \( 0\) , \( 1\) , \( 112\) , \( -4194\bigr] \)
8450.1-a3	\( \bigl[1\) , \( 0\) , \( 1\) , \( -208\) , \( -1122\bigr] \)
8450.1-a4	\( \bigl[1\) , \( 0\) , \( 1\) , \( -33\) , \( 68\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph