Elliptic curve isogeny class 33800.5-d over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-33800.5-d
• Conductor: 33800.5
• Rank: \( 1 \)

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

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

Elliptic curves in class 33800.5-d over \(\Q(\sqrt{-1}) \)

Isogeny class 33800.5-d contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
33800.5-d1	\( \bigl[i + 1\) , \( 0\) , \( i + 1\) , \( -i\) , \( -13 i\bigr] \)
33800.5-d2	\( \bigl[i + 1\) , \( 0\) , \( i + 1\) , \( 69 i - 40\) , \( -281 i - 14\bigr] \)
33800.5-d3	\( \bigl[i + 1\) , \( 0\) , \( i + 1\) , \( -71 i - 40\) , \( -281 i + 14\bigr] \)
33800.5-d4	\( \bigl[i + 1\) , \( 0\) , \( i + 1\) , \( -i + 5\) , \( -4 i\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph