Elliptic curve isogeny class 45000.3-i over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-45000.3-i
• Conductor: 45000.3
• Rank: \( 1 \)

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

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

Elliptic curves in class 45000.3-i over \(\Q(\sqrt{-1}) \)

Isogeny class 45000.3-i contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
45000.3-i1	\( \bigl[i + 1\) , \( -i\) , \( i + 1\) , \( -i - 8\) , \( 8 i\bigr] \)
45000.3-i2	\( \bigl[i + 1\) , \( -i\) , \( i + 1\) , \( -i + 42\) , \( 58 i\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph