Elliptic curve isogeny class 76050.4-e over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-76050.4-e
• Conductor: 76050.4
• Rank: \( 0 \)

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

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

Elliptic curves in class 76050.4-e over \(\Q(\sqrt{-1}) \)

Isogeny class 76050.4-e contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
76050.4-e1	\( \bigl[i\) , \( i\) , \( i\) , \( 314 i + 300\) , \( 3556 i + 3547\bigr] \)
76050.4-e2	\( \bigl[i\) , \( i\) , \( i\) , \( -91 i - 165\) , \( 430 i + 709\bigr] \)
76050.4-e3	\( \bigl[i\) , \( i\) , \( i\) , \( -41 i - 45\) , \( -170 i - 55\bigr] \)
76050.4-e4	\( \bigl[i\) , \( i\) , \( i\) , \( -1296 i - 2550\) , \( 37424 i + 45487\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph