Elliptic curve isogeny class 76050.5-a over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-76050.5-a
• Conductor: 76050.5
• Rank: \( 2 \)

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

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

Elliptic curves in class 76050.5-a over \(\Q(\sqrt{-1}) \)

Isogeny class 76050.5-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
76050.5-a1	\( \bigl[i\) , \( -1\) , \( 0\) , \( 97\) , \( 297\bigr] \)
76050.5-a2	\( \bigl[i\) , \( -1\) , \( 0\) , \( -33\) , \( 63\bigr] \)
76050.5-a3	\( \bigl[i\) , \( -1\) , \( 0\) , \( -13\) , \( -13\bigr] \)
76050.5-a4	\( \bigl[i\) , \( -1\) , \( 0\) , \( -483\) , \( 4293\bigr] \)

Rank

Rank: \( 2 \)

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