Elliptic curve isogeny class 12800.3-a over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-12800.3-a
• Conductor: 12800.3
• Rank: \( 1 \)

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

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

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

Elliptic curves in class 12800.3-a over \(\Q(\sqrt{-1}) \)

Isogeny class 12800.3-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
12800.3-a1	\( \bigl[0\) , \( -1\) , \( 0\) , \( -36 i - 6\) , \( 86 i - 40\bigr] \)
12800.3-a2	\( \bigl[0\) , \( -1\) , \( 0\) , \( 4 i - 36\) , \( 12 i - 72\bigr] \)
12800.3-a3	\( \bigl[0\) , \( -1\) , \( 0\) , \( -i - 1\) , \( 2 i - 2\bigr] \)
12800.3-a4	\( \bigl[0\) , \( 1\) , \( 0\) , \( 14 i + 19\) , \( -18 i + 39\bigr] \)