Elliptic curve isogeny class 7200.2-d over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-7200.2-d
• Conductor: 7200.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 7200.2-d over \(\Q(\sqrt{-2}) \)

Isogeny class 7200.2-d contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
7200.2-d1	\( \bigl[a\) , \( 1\) , \( 0\) , \( 6\) , \( -495\bigr] \)
7200.2-d2	\( \bigl[a\) , \( 1\) , \( a\) , \( -123\) , \( 276\bigr] \)
7200.2-d3	\( \bigl[0\) , \( -1\) , \( 0\) , \( -226\) , \( 1360\bigr] \)
7200.2-d4	\( \bigl[a\) , \( 1\) , \( 0\) , \( 575 a + 506\) , \( 510 a - 11145\bigr] \)
7200.2-d5	\( \bigl[a\) , \( 1\) , \( 0\) , \( -575 a + 506\) , \( -510 a - 11145\bigr] \)
7200.2-d6	\( \bigl[0\) , \( -1\) , \( 0\) , \( -900\) , \( -10098\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph