Elliptic curve isogeny class 41616.3-b over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-41616.3-b
• Conductor: 41616.3
• Rank: \( 0 \)

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

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

Elliptic curves in class 41616.3-b over \(\Q(\sqrt{-2}) \)

Isogeny class 41616.3-b contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
41616.3-b1	\( \bigl[a\) , \( -a + 1\) , \( a\) , \( 357 a - 1760\) , \( 9337 a - 27616\bigr] \)
41616.3-b2	\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -129\) , \( 2656 a - 2091\bigr] \)
41616.3-b3	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 130 a - 407\) , \( -375 a + 4386\bigr] \)
41616.3-b4	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 442 a - 959\) , \( -7773 a + 10272\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 2 & 6 \\ 3 & 1 & 6 & 2 \\ 2 & 6 & 1 & 3 \\ 6 & 2 & 3 & 1 \end{array}\right)\)

Isogeny graph