Elliptic curve isogeny class 25600.1-c over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-25600.1-c
• Conductor: 25600.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 25600.1-c over \(\Q(\sqrt{-1}) \)

Isogeny class 25600.1-c contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
25600.1-c1	\( \bigl[0\) , \( -i + 1\) , \( 0\) , \( 72 i - 8\) , \( -168 i - 120\bigr] \)
25600.1-c2	\( \bigl[0\) , \( -i + 1\) , \( 0\) , \( 12 i + 72\) , \( -252 i + 92\bigr] \)
25600.1-c3	\( \bigl[0\) , \( -i + 1\) , \( 0\) , \( 2 i + 2\) , \( -8 i\bigr] \)
25600.1-c4	\( \bigl[0\) , \( -i - 1\) , \( 0\) , \( 10 i + 7\) , \( -3 i - 13\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph