Elliptic curve isogeny class 6400.2-e over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-6400.2-e
• Conductor: 6400.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 6400.2-e over \(\Q(\sqrt{-1}) \)

Isogeny class 6400.2-e contains 8 curves linked by isogenies of degrees dividing 12.

Curve label	Weierstrass Coefficients
6400.2-e1	\( \bigl[0\) , \( i\) , \( 0\) , \( 20 i - 44\) , \( -92 i + 96\bigr] \)
6400.2-e2	\( \bigl[0\) , \( -i\) , \( 0\) , \( -20 i - 44\) , \( 92 i + 96\bigr] \)
6400.2-e3	\( \bigl[0\) , \( i\) , \( 0\) , \( 220 i - 4\) , \( 948 i + 944\bigr] \)
6400.2-e4	\( \bigl[0\) , \( -i\) , \( 0\) , \( -220 i - 4\) , \( -948 i + 944\bigr] \)
6400.2-e5	\( \bigl[0\) , \( -i\) , \( 0\) , \( 36\) , \( -140 i\bigr] \)
6400.2-e6	\( \bigl[0\) , \( -i\) , \( 0\) , \( -4\) , \( 4 i\bigr] \)
6400.2-e7	\( \bigl[0\) , \( i\) , \( 0\) , \( 1\) , \( 0\bigr] \)
6400.2-e8	\( \bigl[0\) , \( i\) , \( 0\) , \( 41\) , \( 116 i\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 4 & 3 & 12 & 6 & 2 & 4 & 12 \\ 4 & 1 & 12 & 3 & 6 & 2 & 4 & 12 \\ 3 & 12 & 1 & 4 & 2 & 6 & 12 & 4 \\ 12 & 3 & 4 & 1 & 2 & 6 & 12 & 4 \\ 6 & 6 & 2 & 2 & 1 & 3 & 6 & 2 \\ 2 & 2 & 6 & 6 & 3 & 1 & 2 & 6 \\ 4 & 4 & 12 & 12 & 6 & 2 & 1 & 3 \\ 12 & 12 & 4 & 4 & 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph