Elliptic curve isogeny class 16562.2-d over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-16562.2-d
• Conductor: 16562.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 16562.2-d over \(\Q(\sqrt{-1}) \)

Isogeny class 16562.2-d contains 3 curves linked by isogenies of degrees dividing 9.

Curve label	Weierstrass Coefficients
16562.2-d1	\( \bigl[i\) , \( 0\) , \( 0\) , \( -15663\) , \( 755809\bigr] \)
16562.2-d2	\( \bigl[i\) , \( 0\) , \( 0\) , \( -193\) , \( 1055\bigr] \)
16562.2-d3	\( \bigl[i\) , \( 0\) , \( 0\) , \( 7\) , \( 7\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph