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

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-20736.3-g
• 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-g over \(\Q(\sqrt{-2}) \)

Isogeny class 20736.3-g contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
20736.3-g1	\( \bigl[0\) , \( 0\) , \( 0\) , \( 12 a + 9\) , \( -24 a - 26\bigr] \)
20736.3-g2	\( \bigl[0\) , \( 0\) , \( 0\) , \( -3 a - 6\) , \( -3 a - 5\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph