Elliptic curve isogeny class 648.1-a over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-648.1-a
• Conductor: 648.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 648.1-a over \(\Q(\sqrt{-1}) \)

Isogeny class 648.1-a contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
648.1-a1	\( \bigl[i + 1\) , \( i\) , \( 0\) , \( -36\) , \( 572 i\bigr] \)
648.1-a2	\( \bigl[0\) , \( 0\) , \( 0\) , \( 6\) , \( 7\bigr] \)
648.1-a3	\( \bigl[i + 1\) , \( i\) , \( 0\) , \( 9\) , \( -4 i\bigr] \)
648.1-a4	\( \bigl[i + 1\) , \( i\) , \( i + 1\) , \( -i + 54\) , \( -122 i\bigr] \)
648.1-a5	\( \bigl[i + 1\) , \( i\) , \( 0\) , \( 144\) , \( -598 i\bigr] \)
648.1-a6	\( \bigl[i + 1\) , \( i\) , \( i + 1\) , \( -i + 864\) , \( -9356 i\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 8 & 4 \\ 8 & 1 & 2 & 4 & 4 & 8 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 2 & 4 & 2 & 1 & 4 & 2 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 8 & 4 & 2 & 8 & 1 \end{array}\right)\)

Isogeny graph