Elliptic curve isogeny class 52000.4-g over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-52000.4-g
• Conductor: 52000.4
• Rank: \( 1 \)

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

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

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph

Elliptic curves in class 52000.4-g over \(\Q(\sqrt{-1}) \)

Isogeny class 52000.4-g contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
52000.4-g1	\( \bigl[0\) , \( -i\) , \( 0\) , \( -48 i + 22\) , \( -126 i + 2\bigr] \)
52000.4-g2	\( \bigl[0\) , \( -1\) , \( 0\) , \( -58 i + 36\) , \( -8 i - 144\bigr] \)
52000.4-g3	\( \bigl[i + 1\) , \( 0\) , \( i + 1\) , \( 106 i - 49\) , \( 466 i + 55\bigr] \)
52000.4-g4	\( \bigl[i + 1\) , \( -i\) , \( 0\) , \( 202 i - 134\) , \( 1468 i - 101\bigr] \)