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

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

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

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

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

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

Curve label	Weierstrass Coefficients
20736.3-b1	\( \bigl[0\) , \( 0\) , \( 0\) , \( 90 a + 195\) , \( 630 a - 1046\bigr] \)
20736.3-b2	\( \bigl[0\) , \( 0\) , \( 0\) , \( -90 a + 195\) , \( -630 a - 1046\bigr] \)
20736.3-b3	\( \bigl[0\) , \( 0\) , \( 0\) , \( 15\) , \( -38\bigr] \)
20736.3-b4	\( \bigl[0\) , \( 0\) , \( 0\) , \( -30\) , \( 52\bigr] \)

Rank

Rank: \( 2 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph