Elliptic curve isogeny class 28322.3-a over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-28322.3-a
• Conductor: 28322.3
• Rank: \( 0 \)

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

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

Elliptic curves in class 28322.3-a over \(\Q(\sqrt{-2}) \)

Isogeny class 28322.3-a contains 6 curves linked by isogenies of degrees dividing 18.

Curve label	Weierstrass Coefficients
28322.3-a1	\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -2047 a - 170\) , \( -33203 a + 39319\bigr] \)
28322.3-a2	\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -7 a\) , \( 9 a - 11\bigr] \)
28322.3-a3	\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 53 a + 5\) , \( -219 a + 259\bigr] \)
28322.3-a4	\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -427 a - 35\) , \( -2651 a + 3139\bigr] \)
28322.3-a5	\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -127 a - 10\) , \( 465 a - 551\bigr] \)
28322.3-a6	\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -32767 a - 2730\) , \( -2095539 a + 2481559\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 9 & 3 & 6 & 18 & 2 \\ 9 & 1 & 3 & 6 & 2 & 18 \\ 3 & 3 & 1 & 2 & 6 & 6 \\ 6 & 6 & 2 & 1 & 3 & 3 \\ 18 & 2 & 6 & 3 & 1 & 9 \\ 2 & 18 & 6 & 3 & 9 & 1 \end{array}\right)\)

Isogeny graph