Elliptic curve isogeny class 45000.2-b over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-45000.2-b
• Conductor: 45000.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 45000.2-b over \(\Q(\sqrt{-2}) \)

Isogeny class 45000.2-b contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
45000.2-b1	\( \bigl[a\) , \( 1\) , \( a\) , \( -501\) , \( 36999\bigr] \)
45000.2-b2	\( \bigl[a\) , \( 1\) , \( a\) , \( 499\) , \( -751\bigr] \)
45000.2-b3	\( \bigl[a\) , \( 1\) , \( a\) , \( -126\) , \( -126\bigr] \)
45000.2-b4	\( \bigl[a\) , \( 1\) , \( a\) , \( -1251\) , \( 16749\bigr] \)
45000.2-b5	\( \bigl[0\) , \( -1\) , \( 0\) , \( -383\) , \( 3012\bigr] \)
45000.2-b6	\( \bigl[a\) , \( 1\) , \( a\) , \( -20001\) , \( 1085499\bigr] \)

Rank

Rank: \( 1 \)

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