Elliptic curve isogeny class 5184.3-a over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-5184.3-a
• Conductor: 5184.3
• Rank: \( 1 \)

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

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

Elliptic curves in class 5184.3-a over \(\Q(\sqrt{-2}) \)

Isogeny class 5184.3-a contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
5184.3-a1	\( \bigl[a\) , \( -1\) , \( a\) , \( -72 a + 73\) , \( -13 a - 564\bigr] \)
5184.3-a2	\( \bigl[a\) , \( -1\) , \( 0\) , \( 72 a + 72\) , \( -85 a + 493\bigr] \)
5184.3-a3	\( \bigl[a\) , \( -1\) , \( 0\) , \( -27 a - 18\) , \( -67 a + 16\bigr] \)
5184.3-a4	\( \bigl[a\) , \( -1\) , \( a\) , \( 27 a - 17\) , \( -94 a + 3\bigr] \)
5184.3-a5	\( \bigl[0\) , \( 0\) , \( 0\) , \( 18 a + 15\) , \( 14 a - 72\bigr] \)
5184.3-a6	\( \bigl[0\) , \( 0\) , \( 0\) , \( -18 a + 15\) , \( 14 a + 72\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph