Elliptic curve isogeny class 19602.8-g over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-19602.8-g
• Conductor: 19602.8
• Rank: \( 0 \)

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

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

Elliptic curves in class 19602.8-g over \(\Q(\sqrt{-2}) \)

Isogeny class 19602.8-g contains 8 curves linked by isogenies of degrees dividing 12.

Curve label	Weierstrass Coefficients
19602.8-g1	\( \bigl[1\) , \( -1\) , \( 1\) , \( -365\) , \( 15005\bigr] \)
19602.8-g2	\( \bigl[1\) , \( -1\) , \( 1\) , \( 40\) , \( -547\bigr] \)
19602.8-g3	\( \bigl[1\) , \( -1\) , \( 1\) , \( -5310 a + 2515\) , \( -59940 a + 252173\bigr] \)
19602.8-g4	\( \bigl[1\) , \( -1\) , \( 1\) , \( 5310 a + 2515\) , \( 59940 a + 252173\bigr] \)
19602.8-g5	\( \bigl[1\) , \( -1\) , \( 1\) , \( -50\) , \( -115\bigr] \)
19602.8-g6	\( \bigl[1\) , \( -1\) , \( 1\) , \( 585 a + 760\) , \( 3240 a - 13831\bigr] \)
19602.8-g7	\( \bigl[1\) , \( -1\) , \( 1\) , \( -585 a + 760\) , \( -3240 a - 13831\bigr] \)
19602.8-g8	\( \bigl[1\) , \( -1\) , \( 1\) , \( -725\) , \( 7661\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph