Elliptic curve isogeny class 36100.2-b over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-36100.2-b
• Conductor: 36100.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 36100.2-b over \(\Q(\sqrt{-1}) \)

Isogeny class 36100.2-b contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
36100.2-b1	\( \bigl[i + 1\) , \( 0\) , \( 0\) , \( -221\) , \( 5535 i\bigr] \)
36100.2-b2	\( \bigl[0\) , \( -1\) , \( 0\) , \( -921\) , \( 10346\bigr] \)
36100.2-b3	\( \bigl[i + 1\) , \( 0\) , \( 0\) , \( -3895 i - 3831\) , \( 143076 i + 59413\bigr] \)
36100.2-b4	\( \bigl[i + 1\) , \( 0\) , \( 0\) , \( 3895 i - 3831\) , \( 143076 i - 59413\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 2 & 2 \\ 2 & 1 & 4 & 4 \\ 2 & 4 & 1 & 4 \\ 2 & 4 & 4 & 1 \end{array}\right)\)

Isogeny graph