Elliptic curve isogeny class 100.2-a over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-100.2-a
• Conductor: 100.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 100.2-a over \(\Q(\sqrt{-1}) \)

Isogeny class 100.2-a contains 8 curves linked by isogenies of degrees dividing 12.

Curve label	Weierstrass Coefficients
100.2-a1	\( \bigl[i + 1\) , \( -i\) , \( i + 1\) , \( 4 i - 11\) , \( 11 i - 12\bigr] \)
100.2-a2	\( \bigl[i + 1\) , \( 0\) , \( i + 1\) , \( -6 i - 11\) , \( -12 i - 12\bigr] \)
100.2-a3	\( \bigl[i + 1\) , \( -i\) , \( i + 1\) , \( 54 i - 1\) , \( -119 i - 118\bigr] \)
100.2-a4	\( \bigl[i + 1\) , \( 0\) , \( i + 1\) , \( -56 i - 1\) , \( 118 i - 118\bigr] \)
100.2-a5	\( \bigl[i + 1\) , \( 0\) , \( i + 1\) , \( -i + 9\) , \( 17 i\bigr] \)
100.2-a6	\( \bigl[i + 1\) , \( 0\) , \( i + 1\) , \( -i - 1\) , \( -i\bigr] \)
100.2-a7	\( \bigl[0\) , \( 1\) , \( 0\) , \( -1\) , \( 0\bigr] \)
100.2-a8	\( \bigl[0\) , \( 1\) , \( 0\) , \( -41\) , \( -116\bigr] \)

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