Elliptic curve isogeny class 20736.1-d over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-20736.1-d
• Conductor: 20736.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 20736.1-d over \(\Q(\sqrt{-1}) \)

Isogeny class 20736.1-d contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
20736.1-d1	\( \bigl[0\) , \( 0\) , \( 0\) , \( 0\) , \( -i\bigr] \)
20736.1-d2	\( \bigl[0\) , \( 0\) , \( 0\) , \( 0\) , \( 27 i\bigr] \)
20736.1-d3	\( \bigl[0\) , \( 0\) , \( 0\) , \( 135\) , \( 594 i\bigr] \)
20736.1-d4	\( \bigl[0\) , \( 0\) , \( 0\) , \( 15\) , \( -22 i\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph