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

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-19602.8-d
• Conductor: 19602.8
• Rank: \( 1 \)

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

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

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

Isogeny class 19602.8-d contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
19602.8-d1	\( \bigl[1\) , \( -1\) , \( 0\) , \( -108\) , \( 2074\bigr] \)
19602.8-d2	\( \bigl[1\) , \( -1\) , \( 0\) , \( -18\) , \( 4\bigr] \)
19602.8-d3	\( \bigl[1\) , \( -1\) , \( 0\) , \( -1395 a + 612\) , \( -8739 a + 33142\bigr] \)
19602.8-d4	\( \bigl[1\) , \( -1\) , \( 0\) , \( 1395 a + 612\) , \( 8739 a + 33142\bigr] \)
19602.8-d5	\( \bigl[1\) , \( -1\) , \( 0\) , \( -198\) , \( 1120\bigr] \)
19602.8-d6	\( \bigl[1\) , \( -1\) , \( 0\) , \( -3168\) , \( 69430\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 4 & 2 & 2 & 2 & 4 \\ 4 & 1 & 8 & 8 & 2 & 4 \\ 2 & 8 & 1 & 4 & 4 & 8 \\ 2 & 8 & 4 & 1 & 4 & 8 \\ 2 & 2 & 4 & 4 & 1 & 2 \\ 4 & 4 & 8 & 8 & 2 & 1 \end{array}\right)\)

Isogeny graph