Elliptic curve isogeny class 72.2-a over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-72.2-a
• Conductor: 72.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 72.2-a over \(\Q(\sqrt{-2}) \)

Isogeny class 72.2-a contains 8 curves linked by isogenies of degrees dividing 16.

Curve label	Weierstrass Coefficients
72.2-a1	\( \bigl[a\) , \( 1\) , \( a\) , \( 5\) , \( 23\bigr] \)
72.2-a2	\( \bigl[0\) , \( -1\) , \( 0\) , \( 1\) , \( 0\bigr] \)
72.2-a3	\( \bigl[a\) , \( 1\) , \( a\) , \( 0\) , \( 0\bigr] \)
72.2-a4	\( \bigl[a\) , \( 1\) , \( a\) , \( -5\) , \( 5\bigr] \)
72.2-a5	\( \bigl[a\) , \( 1\) , \( a\) , \( 70 a + 85\) , \( -98 a + 559\bigr] \)
72.2-a6	\( \bigl[a\) , \( 1\) , \( a\) , \( -70 a + 85\) , \( 98 a + 559\bigr] \)
72.2-a7	\( \bigl[a\) , \( 1\) , \( a\) , \( -15\) , \( -27\bigr] \)
72.2-a8	\( \bigl[a\) , \( 1\) , \( a\) , \( -95\) , \( 347\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph