Elliptic curve isogeny class 25992.5-c over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-25992.5-c
• Conductor: 25992.5
• Rank: \( 0 \)

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

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

Elliptic curves in class 25992.5-c over \(\Q(\sqrt{-2}) \)

Isogeny class 25992.5-c contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
25992.5-c1	\( \bigl[0\) , \( -1\) , \( 0\) , \( 76 a - 95\) , \( 422 a - 166\bigr] \)
25992.5-c2	\( \bigl[a\) , \( 1\) , \( 0\) , \( 79 a + 1230\) , \( -11696 a + 2435\bigr] \)
25992.5-c3	\( \bigl[a\) , \( 1\) , \( 0\) , \( -581 a + 250\) , \( -2356 a + 9323\bigr] \)
25992.5-c4	\( \bigl[a\) , \( 1\) , \( 0\) , \( -11 a + 60\) , \( -266 a + 203\bigr] \)
25992.5-c5	\( \bigl[a\) , \( 1\) , \( 0\) , \( 19 a - 25\) , \( -51 a + 15\bigr] \)
25992.5-c6	\( \bigl[a\) , \( 1\) , \( 0\) , \( 49 a - 130\) , \( 276 a - 531\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph