Elliptic curve isogeny class 38416.1-b over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-38416.1-b
• Conductor: 38416.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 38416.1-b over \(\Q(\sqrt{-2}) \)

Isogeny class 38416.1-b contains 6 curves linked by isogenies of degrees dividing 18.

Curve label	Weierstrass Coefficients
38416.1-b1	\( \bigl[a\) , \( 0\) , \( a\) , \( -33421\) , \( 2364150\bigr] \)
38416.1-b2	\( \bigl[a\) , \( 0\) , \( a\) , \( -101\) , \( -786\bigr] \)
38416.1-b3	\( \bigl[a\) , \( 0\) , \( a\) , \( 879\) , \( 16658\bigr] \)
38416.1-b4	\( \bigl[a\) , \( 0\) , \( a\) , \( -6961\) , \( 184434\bigr] \)
38416.1-b5	\( \bigl[a\) , \( 0\) , \( a\) , \( -2061\) , \( -35674\bigr] \)
38416.1-b6	\( \bigl[a\) , \( 0\) , \( a\) , \( -535181\) , \( 150784758\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 9 & 3 & 6 & 18 & 2 \\ 9 & 1 & 3 & 6 & 2 & 18 \\ 3 & 3 & 1 & 2 & 6 & 6 \\ 6 & 6 & 2 & 1 & 3 & 3 \\ 18 & 2 & 6 & 3 & 1 & 9 \\ 2 & 18 & 6 & 3 & 9 & 1 \end{array}\right)\)

Isogeny graph