Elliptic curve isogeny class 12544.1-b over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-12544.1-b
• Conductor: 12544.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 12544.1-b over \(\Q(\sqrt{-1}) \)

Isogeny class 12544.1-b contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
12544.1-b1	\( \bigl[0\) , \( -i + 1\) , \( 0\) , \( -3\) , \( i + 1\bigr] \)
12544.1-b2	\( \bigl[0\) , \( -i + 1\) , \( 0\) , \( 10 i - 13\) , \( 31 i - 13\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph