Elliptic curve isogeny class 33800.8-b over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-33800.8-b
• Conductor: 33800.8
• Rank: \( 1 \)

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

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

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph

Elliptic curves in class 33800.8-b over \(\Q(\sqrt{-1}) \)

Isogeny class 33800.8-b contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
33800.8-b1	\( \bigl[i + 1\) , \( i - 1\) , \( 0\) , \( -16197 i + 857\) , \( 521688 i - 597117\bigr] \)
33800.8-b2	\( \bigl[i + 1\) , \( i - 1\) , \( 0\) , \( -2497 i - 3293\) , \( -85724 i - 70383\bigr] \)
33800.8-b3	\( \bigl[i + 1\) , \( i - 1\) , \( 0\) , \( -987 i + 12\) , \( 8097 i - 10180\bigr] \)
33800.8-b4	\( \bigl[0\) , \( -i\) , \( 0\) , \( -236 i - 665\) , \( -3091 i - 10247\bigr] \)