Properties

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

Related objects

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

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

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

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

Curve label Weierstrass Coefficients
82944.1-g1 \( \bigl[0\) , \( 0\) , \( 0\) , \( -282 i\) , \( 9436 i + 9436\bigr] \)
82944.1-g2 \( \bigl[0\) , \( 0\) , \( 0\) , \( -12 i\) , \( -14 i - 14\bigr] \)
82944.1-g3 \( \bigl[0\) , \( 0\) , \( 0\) , \( 78 i\) , \( -140 i - 140\bigr] \)
82944.1-g4 \( \bigl[0\) , \( 0\) , \( 0\) , \( 438 i\) , \( 2380 i + 2380\bigr] \)
82944.1-g5 \( \bigl[0\) , \( 0\) , \( 0\) , \( 1158 i\) , \( -10724 i - 10724\bigr] \)
82944.1-g6 \( \bigl[0\) , \( 0\) , \( 0\) , \( 6918 i\) , \( 156604 i + 156604\bigr] \)

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