Elliptic curve isogeny class 8712.5-a over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-8712.5-a
• Conductor: 8712.5
• Rank: \( 1 \)

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

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

Elliptic curves in class 8712.5-a over \(\Q(\sqrt{-2}) \)

Isogeny class 8712.5-a contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
8712.5-a1	\( \bigl[a\) , \( 1\) , \( 0\) , \( 11 a - 3\) , \( 17 a + 11\bigr] \)
8712.5-a2	\( \bigl[a\) , \( 1\) , \( 0\) , \( 71 a - 158\) , \( -512 a + 635\bigr] \)
8712.5-a3	\( \bigl[a\) , \( 1\) , \( 0\) , \( 11 a - 8\) , \( 10 a + 23\bigr] \)
8712.5-a4	\( \bigl[a\) , \( 1\) , \( 0\) , \( -49 a + 62\) , \( 84 a + 219\bigr] \)
8712.5-a5	\( \bigl[a\) , \( 1\) , \( 0\) , \( -379 a + 282\) , \( 260 a - 5545\bigr] \)
8712.5-a6	\( \bigl[a\) , \( 1\) , \( 0\) , \( -679 a + 962\) , \( 5124 a + 17967\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph