Properties

Base field \(\Q(\sqrt{-1}) \)
Label 2.0.4.1-76050.5-o
Conductor 76050.5
Rank \( 1 \)

Related objects

Learn more about

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

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

Elliptic curves in class 76050.5-o over \(\Q(\sqrt{-1}) \)

Isogeny class 76050.5-o contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
76050.5-o1 \( \bigl[i\) , \( -1\) , \( i\) , \( -114\) , \( 13093\bigr] \)
76050.5-o2 \( \bigl[i\) , \( -1\) , \( i\) , \( 16\) , \( -15\bigr] \)
76050.5-o3 \( \bigl[i\) , \( -1\) , \( i\) , \( -64\) , \( -47\bigr] \)
76050.5-o4 \( \bigl[i\) , \( -1\) , \( i\) , \( -564\) , \( 5353\bigr] \)
76050.5-o5 \( \bigl[i\) , \( -1\) , \( i\) , \( -844\) , \( -9095\bigr] \)
76050.5-o6 \( \bigl[i\) , \( -1\) , \( i\) , \( -9014\) , \( 333213\bigr] \)

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