Elliptic curve isogeny class 16200.3-c over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-16200.3-c
• Conductor: 16200.3
• Rank: \( 0 \)

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

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

Elliptic curves in class 16200.3-c over \(\Q(\sqrt{-2}) \)

Isogeny class 16200.3-c contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
16200.3-c1	\( \bigl[a\) , \( -1\) , \( 0\) , \( 51 a + 114\) , \( 836 a + 707\bigr] \)
16200.3-c2	\( \bigl[a\) , \( -1\) , \( 0\) , \( -39 a - 66\) , \( 188 a + 167\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph