Elliptic curve isogeny class 50020.3-a over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-50020.3-a
• Conductor: 50020.3
• Rank: \( 1 \)

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

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

Elliptic curves in class 50020.3-a over \(\Q(\sqrt{-1}) \)

Isogeny class 50020.3-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
50020.3-a1	\( \bigl[i + 1\) , \( -i\) , \( i + 1\) , \( -20 i + 21\) , \( -53 i + 40\bigr] \)
50020.3-a2	\( \bigl[i + 1\) , \( -i\) , \( i + 1\) , \( 5 i - 9\) , \( -6 i + 8\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph