Elliptic curve isogeny class 42050.5-a over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-42050.5-a
• Conductor: 42050.5
• Rank: \( 1 \)

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

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

Elliptic curves in class 42050.5-a over \(\Q(\sqrt{-1}) \)

Isogeny class 42050.5-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
42050.5-a1	\( \bigl[i\) , \( 1\) , \( 0\) , \( 10\) , \( 700\bigr] \)
42050.5-a2	\( \bigl[i\) , \( 1\) , \( 0\) , \( -70\) , \( 204\bigr] \)
42050.5-a3	\( \bigl[i\) , \( 1\) , \( 0\) , \( 1020 i + 650\) , \( -844 i + 16092\bigr] \)
42050.5-a4	\( \bigl[i\) , \( 1\) , \( 0\) , \( -1020 i + 650\) , \( 844 i + 16092\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph