Elliptic curve isogeny class 8100.2-c over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-8100.2-c
• Conductor: 8100.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 8100.2-c over \(\Q(\sqrt{-1}) \)

Isogeny class 8100.2-c contains 8 curves linked by isogenies of degrees dividing 12.

Curve label	Weierstrass Coefficients
8100.2-c1	\( \bigl[i + 1\) , \( i\) , \( i + 1\) , \( 44 i - 99\) , \( -311 i + 324\bigr] \)
8100.2-c2	\( \bigl[i + 1\) , \( i\) , \( 0\) , \( -45 i - 99\) , \( 212 i + 369\bigr] \)
8100.2-c3	\( \bigl[i + 1\) , \( i\) , \( i + 1\) , \( 494 i - 9\) , \( 3199 i + 3186\bigr] \)
8100.2-c4	\( \bigl[i + 1\) , \( i\) , \( 0\) , \( -495 i - 9\) , \( -3208 i + 3681\bigr] \)
8100.2-c5	\( \bigl[i + 1\) , \( i\) , \( 0\) , \( 81\) , \( -391 i\bigr] \)
8100.2-c6	\( \bigl[i + 1\) , \( i\) , \( 0\) , \( -9\) , \( 5 i\bigr] \)
8100.2-c7	\( \bigl[0\) , \( 0\) , \( 0\) , \( -12\) , \( -11\bigr] \)
8100.2-c8	\( \bigl[0\) , \( 0\) , \( 0\) , \( -372\) , \( 2761\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph