Elliptic curve isogeny class 68450.5-h over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-68450.5-h
• Conductor: 68450.5
• Rank: \( 0 \)

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

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

Elliptic curves in class 68450.5-h over \(\Q(\sqrt{-1}) \)

Isogeny class 68450.5-h contains 8 curves linked by isogenies of degrees dividing 12.

Curve label	Weierstrass Coefficients
68450.5-h1	\( \bigl[i\) , \( 0\) , \( 0\) , \( -920 i + 2805\) , \( 54952 i + 28239\bigr] \)
68450.5-h2	\( \bigl[i\) , \( 0\) , \( 0\) , \( 920 i + 2805\) , \( -54952 i + 28239\bigr] \)
68450.5-h3	\( \bigl[i\) , \( 0\) , \( 0\) , \( -5255\) , \( 149075\bigr] \)
68450.5-h4	\( \bigl[i\) , \( 0\) , \( 0\) , \( 5030 i - 5095\) , \( 293862 i + 186619\bigr] \)
68450.5-h5	\( \bigl[i\) , \( 0\) , \( 0\) , \( -5030 i - 5095\) , \( -293862 i + 186619\bigr] \)
68450.5-h6	\( \bigl[i\) , \( 0\) , \( 0\) , \( 245\) , \( 975\bigr] \)
68450.5-h7	\( \bigl[i\) , \( 0\) , \( 0\) , \( -75\) , \( 143\bigr] \)
68450.5-h8	\( \bigl[i\) , \( 0\) , \( 0\) , \( -5275\) , \( 147903\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 4 & 6 & 3 & 12 & 2 & 4 & 12 \\ 4 & 1 & 6 & 12 & 3 & 2 & 4 & 12 \\ 6 & 6 & 1 & 2 & 2 & 3 & 6 & 2 \\ 3 & 12 & 2 & 1 & 4 & 6 & 12 & 4 \\ 12 & 3 & 2 & 4 & 1 & 6 & 12 & 4 \\ 2 & 2 & 3 & 6 & 6 & 1 & 2 & 6 \\ 4 & 4 & 6 & 12 & 12 & 2 & 1 & 3 \\ 12 & 12 & 2 & 4 & 4 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph