Elliptic curve isogeny class 43218.1-g over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-43218.1-g
• Conductor: 43218.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 43218.1-g over \(\Q(\sqrt{-1}) \)

Isogeny class 43218.1-g contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
43218.1-g1	\( \bigl[i\) , \( 0\) , \( 0\) , \( -197\) , \( 2367\bigr] \)
43218.1-g2	\( \bigl[i\) , \( 0\) , \( 0\) , \( 18913\) , \( 381333\bigr] \)
43218.1-g3	\( \bigl[i\) , \( 0\) , \( 0\) , \( -5097\) , \( 49995\bigr] \)
43218.1-g4	\( \bigl[i\) , \( 0\) , \( 0\) , \( -44787\) , \( -3609423\bigr] \)
43218.1-g5	\( \bigl[i\) , \( 0\) , \( 0\) , \( -4117\) , \( 101935\bigr] \)
43218.1-g6	\( \bigl[i\) , \( 0\) , \( 0\) , \( -65857\) , \( 6510547\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph