Elliptic curve isogeny class 1700.2-b over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-1700.2-b
• Number of curves: 4
• Conductor: 1700.2
• Rank: \( 0 \)

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

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

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph

Elliptic curves in class 1700.2-b over \(\Q(\sqrt{-1}) \)

Isogeny class 1700.2-b contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
1700.2-b1	\( \bigl[0\) , \( -1\) , \( 0\) , \( 4 i - 5\) , \( -8 i + 6\bigr] \)
1700.2-b2	\( \bigl[i + 1\) , \( 0\) , \( 0\) , \( 4 i + 5\) , \( -3 i + 6\bigr] \)
1700.2-b3	\( \bigl[i + 1\) , \( 0\) , \( 0\) , \( 19 i - 15\) , \( -60 i + 7\bigr] \)
1700.2-b4	\( \bigl[i + 1\) , \( 0\) , \( 0\) , \( 69 i + 85\) , \( -216 i + 365\bigr] \)