Elliptic curve isogeny class 99.4-a over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-99.4-a
• Conductor: 99.4
• Rank: \( 0 \)

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

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

Elliptic curves in class 99.4-a over \(\Q(\sqrt{-2}) \)

Isogeny class 99.4-a contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
99.4-a1	\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 10 a - 90\) , \( -72 a + 302\bigr] \)
99.4-a2	\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -5 a + 95\) , \( -252 a - 30\bigr] \)
99.4-a3	\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -5\) , \( -2 a + 4\bigr] \)
99.4-a4	\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( 0\) , \( 0\bigr] \)
99.4-a5	\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -10 a\) , \( -20 a + 22\bigr] \)
99.4-a6	\( \bigl[a + 1\) , \( 1\) , \( a + 1\) , \( -175 a - 15\) , \( -860 a + 1006\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph