Elliptic curve isogeny class 25600.2-p over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-25600.2-p
• Conductor: 25600.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 25600.2-p over \(\Q(\sqrt{-1}) \)

Isogeny class 25600.2-p contains 10 curves linked by isogenies of degrees dividing 16.

Curve label	Weierstrass Coefficients
25600.2-p1	\( \bigl[0\) , \( 0\) , \( 0\) , \( 346 i - 240\) , \( -3316 i + 404\bigr] \)
25600.2-p2	\( \bigl[0\) , \( 0\) , \( 0\) , \( 346 i + 240\) , \( -404 i + 3316\bigr] \)
25600.2-p3	\( \bigl[0\) , \( 0\) , \( 0\) , \( 26 i\) , \( -68 i + 68\bigr] \)
25600.2-p4	\( \bigl[0\) , \( 0\) , \( 0\) , \( 266 i + 480\) , \( 3852 i + 2868\bigr] \)
25600.2-p5	\( \bigl[0\) , \( 0\) , \( 0\) , \( 266 i - 480\) , \( -2868 i - 3852\bigr] \)
25600.2-p6	\( \bigl[0\) , \( 0\) , \( 0\) , \( -14 i\) , \( -12 i + 12\bigr] \)
25600.2-p7	\( \bigl[0\) , \( 0\) , \( 0\) , \( -4 i\) , \( 2 i - 2\bigr] \)
25600.2-p8	\( \bigl[0\) , \( 0\) , \( 0\) , \( -214 i\) , \( -852 i + 852\bigr] \)
25600.2-p9	\( \bigl[0\) , \( 0\) , \( 0\) , \( 5546 i + 3840\) , \( -26164 i + 211636\bigr] \)
25600.2-p10	\( \bigl[0\) , \( 0\) , \( 0\) , \( 5546 i - 3840\) , \( -211636 i + 26164\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph