Elliptic curve isogeny class 9747.5-b over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-9747.5-b
• Conductor: 9747.5
• Rank: \( 0 \)

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

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

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph

Elliptic curves in class 9747.5-b over \(\Q(\sqrt{-2}) \)

Isogeny class 9747.5-b contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
9747.5-b1	\( \bigl[a\) , \( a\) , \( a + 1\) , \( 129 a + 66\) , \( -219 a - 1333\bigr] \)
9747.5-b2	\( \bigl[a\) , \( a\) , \( a + 1\) , \( 71 a - 166\) , \( -712 a + 871\bigr] \)