Elliptic curve isogeny class 8712.1-c over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-8712.1-c
• Conductor: 8712.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 8712.1-c over \(\Q(\sqrt{-1}) \)

Isogeny class 8712.1-c contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
8712.1-c1	\( \bigl[i + 1\) , \( 0\) , \( i + 1\) , \( -i - 22\) , \( 37 i\bigr] \)
8712.1-c2	\( \bigl[i + 1\) , \( -i\) , \( i + 1\) , \( -i + 8\) , \( -8 i\bigr] \)
8712.1-c3	\( \bigl[i + 1\) , \( 0\) , \( i + 1\) , \( -i + 3\) , \( -2 i\bigr] \)
8712.1-c4	\( \bigl[i + 1\) , \( -i\) , \( i + 1\) , \( -i + 118\) , \( -514 i\bigr] \)

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