Elliptic curve isogeny class 10000.1-b over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-10000.1-b
• Conductor: 10000.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 10000.1-b over \(\Q(\sqrt{-2}) \)

Isogeny class 10000.1-b contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
10000.1-b1	\( \bigl[a\) , \( 0\) , \( 0\) , \( -227\) , \( -1961\bigr] \)
10000.1-b2	\( \bigl[a\) , \( 0\) , \( 0\) , \( 23\) , \( 39\bigr] \)
10000.1-b3	\( \bigl[0\) , \( 1\) , \( 0\) , \( -33\) , \( -62\bigr] \)
10000.1-b4	\( \bigl[0\) , \( 1\) , \( 0\) , \( -1033\) , \( 12438\bigr] \)

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