Elliptic curve isogeny class 20736.3-n over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-20736.3-n
• Conductor: 20736.3
• Rank: \( 0 \)

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

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

Elliptic curves in class 20736.3-n over \(\Q(\sqrt{-2}) \)

Isogeny class 20736.3-n contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
20736.3-n1	\( \bigl[0\) , \( 0\) , \( 0\) , \( 0\) , \( -a + 5\bigr] \)
20736.3-n2	\( \bigl[0\) , \( 0\) , \( 0\) , \( 0\) , \( -a - 5\bigr] \)
20736.3-n3	\( \bigl[0\) , \( 0\) , \( 0\) , \( -30 a + 15\) , \( -22 a + 110\bigr] \)
20736.3-n4	\( \bigl[0\) , \( 0\) , \( 0\) , \( 30 a + 15\) , \( -22 a - 110\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph