Elliptic curve isogeny class 8450.5-c over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-8450.5-c
• Conductor: 8450.5
• Rank: \( 0 \)

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

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

Elliptic curves in class 8450.5-c over \(\Q(\sqrt{-1}) \)

Isogeny class 8450.5-c contains 10 curves linked by isogenies of degrees dividing 16.

Curve label	Weierstrass Coefficients
8450.5-c1	\( \bigl[i\) , \( 1\) , \( i\) , \( 10185 i + 1329\) , \( 225750 i + 333071\bigr] \)
8450.5-c2	\( \bigl[i\) , \( 1\) , \( i\) , \( -10185 i + 1329\) , \( -225750 i + 333071\bigr] \)
8450.5-c3	\( \bigl[i\) , \( 1\) , \( i\) , \( -630 i + 94\) , \( -3892 i + 5185\bigr] \)
8450.5-c4	\( \bigl[i\) , \( 1\) , \( i\) , \( 630 i + 94\) , \( 3892 i + 5185\bigr] \)
8450.5-c5	\( \bigl[i\) , \( 1\) , \( i\) , \( -66\) , \( 441\bigr] \)
8450.5-c6	\( \bigl[i\) , \( 1\) , \( i\) , \( 1155 i + 1419\) , \( 23562 i - 21005\bigr] \)
8450.5-c7	\( \bigl[i\) , \( 1\) , \( i\) , \( -1155 i + 1419\) , \( -23562 i - 21005\bigr] \)
8450.5-c8	\( \bigl[i\) , \( 1\) , \( i\) , \( -6\) , \( 1\bigr] \)
8450.5-c9	\( \bigl[i\) , \( 1\) , \( i\) , \( -86\) , \( 289\bigr] \)
8450.5-c10	\( \bigl[i\) , \( 1\) , \( i\) , \( -1386\) , \( 19529\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrrrr} 1 & 16 & 8 & 2 & 4 & 4 & 16 & 16 & 8 & 16 \\ 16 & 1 & 2 & 8 & 4 & 16 & 4 & 16 & 8 & 16 \\ 8 & 2 & 1 & 4 & 2 & 8 & 2 & 8 & 4 & 8 \\ 2 & 8 & 4 & 1 & 2 & 2 & 8 & 8 & 4 & 8 \\ 4 & 4 & 2 & 2 & 1 & 4 & 4 & 4 & 2 & 4 \\ 4 & 16 & 8 & 2 & 4 & 1 & 16 & 16 & 8 & 16 \\ 16 & 4 & 2 & 8 & 4 & 16 & 1 & 16 & 8 & 16 \\ 16 & 16 & 8 & 8 & 4 & 16 & 16 & 1 & 2 & 4 \\ 8 & 8 & 4 & 4 & 2 & 8 & 8 & 2 & 1 & 2 \\ 16 & 16 & 8 & 8 & 4 & 16 & 16 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph