Elliptic curve isogeny class 16640.3-g over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-16640.3-g
• Number of curves: 6
• Conductor: 16640.3
• Rank: \( 0 \)

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

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

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph

Elliptic curves in class 16640.3-g over \(\Q(\sqrt{-1}) \)

Isogeny class 16640.3-g contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
16640.3-g1	\( \bigl[0\) , \( 0\) , \( 0\) , \( 24 i - 1\) , \( -34 i - 30\bigr] \)
16640.3-g2	\( \bigl[0\) , \( 0\) , \( 0\) , \( -36 i - 41\) , \( 138 i + 76\bigr] \)
16640.3-g3	\( \bigl[0\) , \( 0\) , \( 0\) , \( 24 i - 61\) , \( -446 i + 120\bigr] \)
16640.3-g4	\( \bigl[0\) , \( 0\) , \( 0\) , \( -6 i - 1\) , \( 2 i - 6\bigr] \)
16640.3-g5	\( \bigl[0\) , \( 0\) , \( 0\) , \( 24 i + 19\) , \( 30 i - 48\bigr] \)
16640.3-g6	\( \bigl[0\) , \( 0\) , \( 0\) , \( -576 i - 661\) , \( 8790 i + 4752\bigr] \)