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

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

Isogeny class 82944.1-n contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
82944.1-n1	\( \bigl[0\) , \( 0\) , \( 0\) , \( 282 i\) , \( -9436 i + 9436\bigr] \)
82944.1-n2	\( \bigl[0\) , \( 0\) , \( 0\) , \( 12 i\) , \( 14 i - 14\bigr] \)
82944.1-n3	\( \bigl[0\) , \( 0\) , \( 0\) , \( -78 i\) , \( 140 i - 140\bigr] \)
82944.1-n4	\( \bigl[0\) , \( 0\) , \( 0\) , \( -438 i\) , \( -2380 i + 2380\bigr] \)
82944.1-n5	\( \bigl[0\) , \( 0\) , \( 0\) , \( -1158 i\) , \( 10724 i - 10724\bigr] \)
82944.1-n6	\( \bigl[0\) , \( 0\) , \( 0\) , \( -6918 i\) , \( -156604 i + 156604\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 8 & 4 \\ 8 & 1 & 2 & 4 & 4 & 8 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 2 & 4 & 2 & 1 & 4 & 2 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 8 & 4 & 2 & 8 & 1 \end{array}\right)\)

Isogeny graph