Elliptic curve isogeny class 52000.6-c over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-52000.6-c
• Conductor: 52000.6
• Rank: \( 0 \)

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

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

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph

Elliptic curves in class 52000.6-c over \(\Q(\sqrt{-1}) \)

Isogeny class 52000.6-c contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
52000.6-c1	\( \bigl[0\) , \( -1\) , \( 0\) , \( -8 i - 52\) , \( -102 i + 76\bigr] \)
52000.6-c2	\( \bigl[0\) , \( i\) , \( 0\) , \( -18 i - 66\) , \( -94 i - 108\bigr] \)
52000.6-c3	\( \bigl[i + 1\) , \( i - 1\) , \( i + 1\) , \( 15 i + 116\) , \( 522 i - 146\bigr] \)
52000.6-c4	\( \bigl[i + 1\) , \( i + 1\) , \( i + 1\) , \( 72 i + 231\) , \( 1445 i - 594\bigr] \)