Properties

Base field \(\Q(\sqrt{-1}) \)
Label 2.0.4.1-50005.3-a
Conductor 50005.3
Rank \( 0 \)

Related objects

Learn more

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

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

Elliptic curves in class 50005.3-a over \(\Q(\sqrt{-1}) \)

Isogeny class 50005.3-a contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
50005.3-a1 \( \bigl[i\) , \( i - 1\) , \( i\) , \( 732 i - 202\) , \( -7865 i - 3158\bigr] \)
50005.3-a2 \( \bigl[1\) , \( -i + 1\) , \( 1\) , \( 717 i - 163\) , \( 8651 i + 2668\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph