Elliptic curve isogeny class 676.2-a over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-676.2-a
• Conductor: 676.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 676.2-a over \(\Q(\sqrt{-1}) \)

Isogeny class 676.2-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
676.2-a1	\( \bigl[i + 1\) , \( i\) , \( i + 1\) , \( -i - 1\) , \( -2 i\bigr] \)
676.2-a2	\( \bigl[0\) , \( 0\) , \( 0\) , \( -4\) , \( 3\bigr] \)
676.2-a3	\( \bigl[i + 1\) , \( i\) , \( i + 1\) , \( -16 i - 11\) , \( -35 i + 4\bigr] \)
676.2-a4	\( \bigl[i + 1\) , \( i\) , \( i + 1\) , \( 14 i - 11\) , \( -35 i - 4\bigr] \)

Rank

Rank: \( 0 \)

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