Elliptic curve isogeny class 38025.5-a over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-38025.5-a
• Conductor: 38025.5
• Rank: \( 0 \)

Base field \(\Q(\sqrt{-1}) \)

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

Elliptic curves in class 38025.5-a over \(\Q(\sqrt{-1}) \)

Isogeny class 38025.5-a contains 10 curves linked by isogenies of degrees dividing 16.

Curve label	Weierstrass Coefficients
38025.5-a1	\( \bigl[i\) , \( 0\) , \( 0\) , \( 8925 i + 9605\) , \( -254835 i + 518800\bigr] \)
38025.5-a2	\( \bigl[i\) , \( 0\) , \( 0\) , \( -8925 i + 9605\) , \( 254835 i + 518800\bigr] \)
38025.5-a3	\( \bigl[i\) , \( 0\) , \( 0\) , \( -7930\) , \( 296725\bigr] \)
38025.5-a4	\( \bigl[i\) , \( 0\) , \( 0\) , \( 605\) , \( 19750\bigr] \)
38025.5-a5	\( \bigl[i\) , \( 0\) , \( 0\) , \( 210\) , \( -2277\bigr] \)
38025.5-a6	\( \bigl[i\) , \( 0\) , \( 0\) , \( -115\) , \( -392\bigr] \)
38025.5-a7	\( \bigl[i\) , \( 0\) , \( 0\) , \( -520\) , \( 4225\bigr] \)
38025.5-a8	\( \bigl[i\) , \( 0\) , \( 0\) , \( -110\) , \( -435\bigr] \)
38025.5-a9	\( \bigl[i\) , \( 0\) , \( 0\) , \( -8125\) , \( 282568\bigr] \)
38025.5-a10	\( \bigl[i\) , \( 0\) , \( 0\) , \( -130000\) , \( 18051943\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph