Elliptic curve isogeny class 38025.2-a over number field \(\Q(\sqrt{-2}) \)

• Base field: \(\Q(\sqrt{-2}) \)
• Label: 2.0.8.1-38025.2-a
• Conductor: 38025.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 38025.2-a over \(\Q(\sqrt{-2}) \)

Isogeny class 38025.2-a contains 8 curves linked by isogenies of degrees dividing 16.

Curve label	Weierstrass Coefficients
38025.2-a1	\( \bigl[1\) , \( 0\) , \( 0\) , \( -7930\) , \( -296725\bigr] \)
38025.2-a2	\( \bigl[1\) , \( 0\) , \( 0\) , \( 605\) , \( -19750\bigr] \)
38025.2-a3	\( \bigl[1\) , \( 0\) , \( 0\) , \( 210\) , \( 2277\bigr] \)
38025.2-a4	\( \bigl[1\) , \( 0\) , \( 0\) , \( -115\) , \( 392\bigr] \)
38025.2-a5	\( \bigl[1\) , \( 0\) , \( 0\) , \( -520\) , \( -4225\bigr] \)
38025.2-a6	\( \bigl[1\) , \( 0\) , \( 0\) , \( -110\) , \( 435\bigr] \)
38025.2-a7	\( \bigl[1\) , \( 0\) , \( 0\) , \( -8125\) , \( -282568\bigr] \)
38025.2-a8	\( \bigl[1\) , \( 0\) , \( 0\) , \( -130000\) , \( -18051943\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph