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

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-32400.3-b
• Conductor: 32400.3
• Rank: \( 0 \)

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

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

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

Isogeny class 32400.3-b contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
32400.3-b1	\( \bigl[i + 1\) , \( i\) , \( 0\) , \( -141 i + 105\) , \( 6540 i - 1109\bigr] \)
32400.3-b2	\( \bigl[0\) , \( 0\) , \( 0\) , \( 24 i - 18\) , \( -14 i - 77\bigr] \)
32400.3-b3	\( \bigl[i + 1\) , \( i\) , \( 0\) , \( 39 i - 30\) , \( -111 i - 2\bigr] \)
32400.3-b4	\( \bigl[i + 1\) , \( i\) , \( 0\) , \( 219 i - 165\) , \( 1554 i - 407\bigr] \)
32400.3-b5	\( \bigl[i + 1\) , \( i\) , \( 0\) , \( 579 i - 435\) , \( -7590 i + 1051\bigr] \)
32400.3-b6	\( \bigl[i + 1\) , \( i\) , \( 0\) , \( 3459 i - 2595\) , \( 106368 i - 21305\bigr] \)

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