Elliptic curve isogeny class 648.3-a over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-648.3-a
• Conductor: 648.3
• Rank: \( 1 \)

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

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

Elliptic curves in class 648.3-a over \(\Q(\sqrt{-2}) \)

Isogeny class 648.3-a contains 8 curves linked by isogenies of degrees dividing 16.

Curve label	Weierstrass Coefficients
648.3-a1	\( \bigl[a\) , \( -1\) , \( a\) , \( 37\) , \( -607\bigr] \)
648.3-a2	\( \bigl[0\) , \( 0\) , \( 0\) , \( 6\) , \( -7\bigr] \)
648.3-a3	\( \bigl[a\) , \( -1\) , \( a\) , \( -8\) , \( 14\bigr] \)
648.3-a4	\( \bigl[a\) , \( -1\) , \( a\) , \( -53\) , \( -121\bigr] \)
648.3-a5	\( \bigl[a\) , \( -1\) , \( a\) , \( 630 a + 757\) , \( 2646 a - 15079\bigr] \)
648.3-a6	\( \bigl[a\) , \( -1\) , \( a\) , \( -630 a + 757\) , \( -2646 a - 15079\bigr] \)
648.3-a7	\( \bigl[a\) , \( -1\) , \( a\) , \( -143\) , \( 743\bigr] \)
648.3-a8	\( \bigl[a\) , \( -1\) , \( a\) , \( -863\) , \( -9355\bigr] \)

Rank

Rank: \( 1 \)

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