Elliptic curve isogeny class 178.1-a over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-178.1-a
• Conductor: 178.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 178.1-a over \(\Q(\sqrt{-2}) \)

Isogeny class 178.1-a contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
178.1-a1	\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( -2 a - 2\) , \( 1\bigr] \)
178.1-a2	\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( -17 a + 8\) , \( 6 a + 55\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph