Elliptic curve isogeny class 3400.4-b over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-3400.4-b
• Conductor: 3400.4
• Rank: \( 0 \)

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

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

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph

Elliptic curves in class 3400.4-b over \(\Q(\sqrt{-1}) \)

Isogeny class 3400.4-b contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
3400.4-b1	\( \bigl[i + 1\) , \( -i - 1\) , \( i + 1\) , \( -534 i - 133\) , \( 4733 i - 2059\bigr] \)
3400.4-b2	\( \bigl[i + 1\) , \( 1\) , \( i + 1\) , \( -34 i - 8\) , \( -84 i + 34\bigr] \)
3400.4-b3	\( \bigl[i + 1\) , \( 1\) , \( i + 1\) , \( 86 i - 573\) , \( -1236 i + 5043\bigr] \)
3400.4-b4	\( \bigl[i + 1\) , \( 1\) , \( i + 1\) , \( -14 i - 23\) , \( -116 i + 133\bigr] \)
3400.4-b5	\( \bigl[0\) , \( i + 1\) , \( 0\) , \( 14 i - 2\) , \( -8 i + 1\bigr] \)
3400.4-b6	\( \bigl[i + 1\) , \( 1\) , \( i + 1\) , \( 206 i + 287\) , \( -1244 i + 1959\bigr] \)