Elliptic curve isogeny class 12800.2-e over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-12800.2-e
• Conductor: 12800.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 12800.2-e over \(\Q(\sqrt{-1}) \)

Isogeny class 12800.2-e contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
12800.2-e1	\( \bigl[0\) , \( -i + 1\) , \( 0\) , \( 2 i - 35\) , \( -i + 83\bigr] \)
12800.2-e2	\( \bigl[0\) , \( -i + 1\) , \( 0\) , \( 2 i + 35\) , \( 83 i - 1\bigr] \)
12800.2-e3	\( \bigl[0\) , \( -i + 1\) , \( 0\) , \( 7 i\) , \( 10 i + 10\bigr] \)
12800.2-e4	\( \bigl[0\) , \( i - 1\) , \( 0\) , \( 132 i\) , \( -460 i - 460\bigr] \)

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