Elliptic curve isogeny class 14450.5-d over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-14450.5-d
• Conductor: 14450.5
• Rank: \( 1 \)

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

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

Elliptic curves in class 14450.5-d over \(\Q(\sqrt{-1}) \)

Isogeny class 14450.5-d contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
14450.5-d1	\( \bigl[i\) , \( 0\) , \( i\) , \( 130 i + 173\) , \( 688 i - 1022\bigr] \)
14450.5-d2	\( \bigl[i\) , \( 0\) , \( i\) , \( -130 i + 173\) , \( -688 i - 1022\bigr] \)
14450.5-d3	\( \bigl[i\) , \( 0\) , \( i\) , \( 13\) , \( -38\bigr] \)
14450.5-d4	\( \bigl[i\) , \( 0\) , \( i\) , \( -7\) , \( -6\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph