Elliptic curve isogeny class 82944.1-o over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-82944.1-o
• Conductor: 82944.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 82944.1-o over \(\Q(\sqrt{-1}) \)

Isogeny class 82944.1-o contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
82944.1-o1	\( \bigl[0\) , \( 0\) , \( 0\) , \( -138 i\) , \( 292 i + 292\bigr] \)
82944.1-o2	\( \bigl[0\) , \( 0\) , \( 0\) , \( 42 i\) , \( 40 i + 40\bigr] \)
82944.1-o3	\( \bigl[0\) , \( 0\) , \( 0\) , \( -78 i\) , \( -184 i + 184\bigr] \)
82944.1-o4	\( \bigl[0\) , \( 0\) , \( 0\) , \( 582 i\) , \( -3820 i - 3820\bigr] \)

Rank

Rank: \( 0 \)

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