Elliptic curve isogeny class 32400.3-c over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-32400.3-c
• Conductor: 32400.3
• Rank: \( 1 \)

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

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

Elliptic curves in class 32400.3-c over \(\Q(\sqrt{-1}) \)

Isogeny class 32400.3-c contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
32400.3-c1	\( \bigl[0\) , \( 0\) , \( 0\) , \( 0\) , \( 54 i + 297\bigr] \)
32400.3-c2	\( \bigl[0\) , \( 0\) , \( 0\) , \( 0\) , \( -2 i - 11\bigr] \)
32400.3-c3	\( \bigl[i + 1\) , \( i\) , \( 0\) , \( 15 i - 12\) , \( -36 i - 2\bigr] \)
32400.3-c4	\( \bigl[i + 1\) , \( i\) , \( 0\) , \( 135 i - 102\) , \( 766 i - 216\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph