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

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-16562.2-e
• 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-e over \(\Q(\sqrt{-1}) \)

Isogeny class 16562.2-e contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
16562.2-e1	\( \bigl[i\) , \( 1\) , \( i\) , \( 867\) , \( -6445\bigr] \)
16562.2-e2	\( \bigl[i\) , \( 1\) , \( i\) , \( -4253\) , \( -59693\bigr] \)
16562.2-e3	\( \bigl[i\) , \( 1\) , \( i\) , \( -31293\) , \( 2081875\bigr] \)
16562.2-e4	\( \bigl[i\) , \( 1\) , \( i\) , \( -59133\) , \( -5547693\bigr] \)

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