Elliptic curve isogeny class 5202.2-d over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-5202.2-d
• Conductor: 5202.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 5202.2-d over \(\Q(\sqrt{-1}) \)

Isogeny class 5202.2-d contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
5202.2-d1	\( \bigl[i\) , \( i\) , \( 0\) , \( -1584 i + 80\) , \( -15675 i + 18965\bigr] \)
5202.2-d2	\( \bigl[1\) , \( -i\) , \( 0\) , \( -99 i + 5\) , \( 240 i - 320\bigr] \)
5202.2-d3	\( \bigl[1\) , \( -i\) , \( 0\) , \( -54 i - 70\) , \( 141 i - 971\bigr] \)
5202.2-d4	\( \bigl[i\) , \( i\) , \( 0\) , \( -9 i + 5\) , \( -6 i - 4\bigr] \)

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