Elliptic curve isogeny class 66049.1-a over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-66049.1-a
• Conductor: 66049.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 66049.1-a over \(\Q(\sqrt{-1}) \)

Isogeny class 66049.1-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
66049.1-a1	\( \bigl[1\) , \( 1\) , \( 1\) , \( -255 i - 1344\) , \( 5355 i + 18401\bigr] \)
66049.1-a2	\( \bigl[1\) , \( 1\) , \( 1\) , \( 1020 i - 1504\) , \( 44115 i + 13537\bigr] \)
66049.1-a3	\( \bigl[1\) , \( 1\) , \( 1\) , \( -95 i - 69\) , \( -519 i + 489\bigr] \)
66049.1-a4	\( \bigl[1\) , \( 1\) , \( 1\) , \( -4090 i - 21584\) , \( 345731 i + 1195133\bigr] \)

Rank

Rank: \( 1 \)

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