Elliptic curve isogeny class 50176.1-e over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-50176.1-e
• Conductor: 50176.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 50176.1-e over \(\Q(\sqrt{-1}) \)

Isogeny class 50176.1-e contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
50176.1-e1	\( \bigl[0\) , \( 0\) , \( 0\) , \( -2 i\) , \( -4 i - 4\bigr] \)
50176.1-e2	\( \bigl[0\) , \( 0\) , \( 0\) , \( 118 i\) , \( 276 i + 276\bigr] \)
50176.1-e3	\( \bigl[0\) , \( 0\) , \( 0\) , \( 38 i\) , \( -60 i - 60\bigr] \)
50176.1-e4	\( \bigl[0\) , \( 0\) , \( 0\) , \( 598 i\) , \( -3980 i - 3980\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph