Elliptic curve isogeny class 2592.3-f over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-2592.3-f
• Conductor: 2592.3
• Rank: \( 0 \)

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

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

Elliptic curves in class 2592.3-f over \(\Q(\sqrt{-2}) \)

Isogeny class 2592.3-f contains 8 curves linked by isogenies of degrees dividing 16.

Curve label	Weierstrass Coefficients
2592.3-f1	\( \bigl[a\) , \( -1\) , \( a\) , \( 720 a - 287\) , \( -9094 a - 4659\bigr] \)
2592.3-f2	\( \bigl[a\) , \( -1\) , \( 0\) , \( -720 a - 288\) , \( -8374 a + 4948\bigr] \)
2592.3-f3	\( \bigl[0\) , \( 0\) , \( 0\) , \( 15\) , \( 68 a\bigr] \)
2592.3-f4	\( \bigl[a\) , \( -1\) , \( 0\) , \( -90 a - 108\) , \( 446 a + 448\bigr] \)
2592.3-f5	\( \bigl[a\) , \( -1\) , \( a\) , \( 90 a - 107\) , \( 356 a - 339\bigr] \)
2592.3-f6	\( \bigl[a\) , \( -1\) , \( a\) , \( 45 a - 17\) , \( -157 a - 69\bigr] \)
2592.3-f7	\( \bigl[a\) , \( -1\) , \( 0\) , \( -45 a - 18\) , \( -112 a + 88\bigr] \)
2592.3-f8	\( \bigl[0\) , \( 0\) , \( 0\) , \( 105\) , \( -292 a\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 16 & 4 & 16 & 4 & 2 & 8 & 8 \\ 16 & 1 & 4 & 4 & 16 & 8 & 2 & 8 \\ 4 & 4 & 1 & 4 & 4 & 2 & 2 & 2 \\ 16 & 4 & 4 & 1 & 16 & 8 & 2 & 8 \\ 4 & 16 & 4 & 16 & 1 & 2 & 8 & 8 \\ 2 & 8 & 2 & 8 & 2 & 1 & 4 & 4 \\ 8 & 2 & 2 & 2 & 8 & 4 & 1 & 4 \\ 8 & 8 & 2 & 8 & 8 & 4 & 4 & 1 \end{array}\right)\)

Isogeny graph