Elliptic curve isogeny class 46818.8-s over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-46818.8-s
• Conductor: 46818.8
• Rank: \( 0 \)

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

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

Elliptic curves in class 46818.8-s over \(\Q(\sqrt{-2}) \)

Isogeny class 46818.8-s contains 8 curves linked by isogenies of degrees dividing 12.

Curve label	Weierstrass Coefficients
46818.8-s1	\( \bigl[1\) , \( -1\) , \( 1\) , \( -77040 a + 200605\) , \( 21906720 a + 28585379\bigr] \)
46818.8-s2	\( \bigl[1\) , \( -1\) , \( 1\) , \( 77040 a + 200605\) , \( -21906720 a + 28585379\bigr] \)
46818.8-s3	\( \bigl[1\) , \( -1\) , \( 1\) , \( -9810 a + 940\) , \( 328320 a - 495889\bigr] \)
46818.8-s4	\( \bigl[1\) , \( -1\) , \( 1\) , \( 9810 a + 940\) , \( -328320 a - 495889\bigr] \)
46818.8-s5	\( \bigl[1\) , \( -1\) , \( 1\) , \( -1940\) , \( -55681\bigr] \)
46818.8-s6	\( \bigl[1\) , \( -1\) , \( 1\) , \( 16285\) , \( 1020323\bigr] \)
46818.8-s7	\( \bigl[1\) , \( -1\) , \( 1\) , \( -6755\) , \( 163235\bigr] \)
46818.8-s8	\( \bigl[1\) , \( -1\) , \( 1\) , \( -2300\) , \( -41857\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 4 & 3 & 12 & 6 & 2 & 4 & 12 \\ 4 & 1 & 12 & 3 & 6 & 2 & 4 & 12 \\ 3 & 12 & 1 & 4 & 2 & 6 & 12 & 4 \\ 12 & 3 & 4 & 1 & 2 & 6 & 12 & 4 \\ 6 & 6 & 2 & 2 & 1 & 3 & 6 & 2 \\ 2 & 2 & 6 & 6 & 3 & 1 & 2 & 6 \\ 4 & 4 & 12 & 12 & 6 & 2 & 1 & 3 \\ 12 & 12 & 4 & 4 & 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph