Elliptic curve isogeny class 41616.5-j over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-41616.5-j
• Conductor: 41616.5
• Rank: \( 1 \)

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

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

Elliptic curves in class 41616.5-j over \(\Q(\sqrt{-2}) \)

Isogeny class 41616.5-j contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
41616.5-j1	\( \bigl[0\) , \( a\) , \( 0\) , \( -22 a + 62\) , \( -102 a - 129\bigr] \)
41616.5-j2	\( \bigl[a\) , \( a - 1\) , \( a\) , \( 51 a + 143\) , \( -396 a + 422\bigr] \)
41616.5-j3	\( \bigl[a\) , \( a - 1\) , \( a\) , \( -4 a + 18\) , \( 18 a + 23\bigr] \)
41616.5-j4	\( \bigl[a\) , \( a - 1\) , \( a\) , \( -19 a - 87\) , \( 120 a + 278\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph