Elliptic curve isogeny class 1690.4-a over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-1690.4-a
• Conductor: 1690.4
• Rank: \( 0 \)

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

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

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 7 & 21 & 3 \\ 7 & 1 & 3 & 21 \\ 21 & 3 & 1 & 7 \\ 3 & 21 & 7 & 1 \end{array}\right)\)

Isogeny graph

Elliptic curves in class 1690.4-a over \(\Q(\sqrt{-1}) \)

Isogeny class 1690.4-a contains 4 curves linked by isogenies of degrees dividing 21.

Curve label	Weierstrass Coefficients
1690.4-a1	\( \bigl[1\) , \( i - 1\) , \( 0\) , \( 5 i - 13\) , \( -8 i - 2\bigr] \)
1690.4-a2	\( \bigl[i\) , \( -i + 1\) , \( 0\) , \( 835 i + 627\) , \( 3158 i - 11704\bigr] \)
1690.4-a3	\( \bigl[i\) , \( -i + 1\) , \( 0\) , \( -9445 i + 4347\) , \( 35678 i - 394688\bigr] \)
1690.4-a4	\( \bigl[1\) , \( i - 1\) , \( 0\) , \( 370 i - 658\) , \( -5867 i + 5777\bigr] \)