Elliptic curve isogeny class 16900.5-a over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-16900.5-a
• Conductor: 16900.5
• Rank: \( 0 \)

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

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

Elliptic curves in class 16900.5-a over \(\Q(\sqrt{-1}) \)

Isogeny class 16900.5-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
16900.5-a1	\( \bigl[i + 1\) , \( 0\) , \( 0\) , \( 69\) , \( 247 i\bigr] \)
16900.5-a2	\( \bigl[i + 1\) , \( 0\) , \( 0\) , \( -145 i + 59\) , \( 516 i - 943\bigr] \)
16900.5-a3	\( \bigl[i + 1\) , \( 0\) , \( 0\) , \( 145 i + 59\) , \( 516 i + 943\bigr] \)
16900.5-a4	\( \bigl[0\) , \( -1\) , \( 0\) , \( -281\) , \( 1910\bigr] \)

Rank

Rank: \( 0 \)

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