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

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

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

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

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

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

Curve label	Weierstrass Coefficients
82944.1-q1	\( \bigl[0\) , \( 0\) , \( 0\) , \( 90 i + 96\) , \( 252 i - 524\bigr] \)
82944.1-q2	\( \bigl[0\) , \( 0\) , \( 0\) , \( -90 i + 96\) , \( -252 i - 524\bigr] \)
82944.1-q3	\( \bigl[0\) , \( 0\) , \( 0\) , \( 6\) , \( -20\bigr] \)
82944.1-q4	\( \bigl[0\) , \( 0\) , \( 0\) , \( 21\) , \( 34 i\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph