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

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-82944.1-j
• 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-j over \(\Q(\sqrt{-1}) \)

Isogeny class 82944.1-j contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
82944.1-j1	\( \bigl[0\) , \( 0\) , \( 0\) , \( 0\) , \( -2 i - 2\bigr] \)
82944.1-j2	\( \bigl[0\) , \( 0\) , \( 0\) , \( 0\) , \( 54 i + 54\bigr] \)
82944.1-j3	\( \bigl[0\) , \( 0\) , \( 0\) , \( 270 i\) , \( 1188 i + 1188\bigr] \)
82944.1-j4	\( \bigl[0\) , \( 0\) , \( 0\) , \( 30 i\) , \( -44 i - 44\bigr] \)

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