Elliptic curve isogeny class 2450.2-a over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-2450.2-a
• Conductor: 2450.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 2450.2-a over \(\Q(\sqrt{-1}) \)

Isogeny class 2450.2-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
2450.2-a1	\( \bigl[i\) , \( 1\) , \( i\) , \( 3\) , \( 3\bigr] \)
2450.2-a2	\( \bigl[i\) , \( 1\) , \( i\) , \( -17\) , \( 19\bigr] \)
2450.2-a3	\( \bigl[i\) , \( 1\) , \( i\) , \( -87\) , \( -317\bigr] \)
2450.2-a4	\( \bigl[i\) , \( 1\) , \( i\) , \( -267\) , \( 1619\bigr] \)

Rank

Rank: \( 1 \)

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