Elliptic curve isogeny class 39204.1-c over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-39204.1-c
• Conductor: 39204.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 39204.1-c over \(\Q(\sqrt{-2}) \)

Isogeny class 39204.1-c contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
39204.1-c1	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -110 a - 116\) , \( -568 a - 93\bigr] \)
39204.1-c2	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -162 a - 96\) , \( -1082 a + 477\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph