Elliptic curve isogeny class 45000.3-e over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-45000.3-e
• Conductor: 45000.3
• Rank: \( 1 \)

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

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

Elliptic curves in class 45000.3-e over \(\Q(\sqrt{-1}) \)

Isogeny class 45000.3-e contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
45000.3-e1	\( \bigl[i + 1\) , \( 0\) , \( i + 1\) , \( -i + 502\) , \( -36999 i\bigr] \)
45000.3-e2	\( \bigl[i + 1\) , \( 0\) , \( i + 1\) , \( -i - 498\) , \( 751 i\bigr] \)
45000.3-e3	\( \bigl[i + 1\) , \( 0\) , \( i + 1\) , \( -i + 127\) , \( 126 i\bigr] \)
45000.3-e4	\( \bigl[i + 1\) , \( 0\) , \( i + 1\) , \( -i + 1252\) , \( -16749 i\bigr] \)
45000.3-e5	\( \bigl[0\) , \( -1\) , \( 0\) , \( -383\) , \( 3012\bigr] \)
45000.3-e6	\( \bigl[i + 1\) , \( 0\) , \( i + 1\) , \( -i + 20002\) , \( -1085499 i\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph