Elliptic curve isogeny class 40000.3-g over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-40000.3-g
• Conductor: 40000.3
• Rank: \( 1 \)

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

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

Elliptic curves in class 40000.3-g over \(\Q(\sqrt{-1}) \)

Isogeny class 40000.3-g contains 2 curves linked by isogenies of degree 5.

Curve label	Weierstrass Coefficients
40000.3-g1	\( \bigl[i + 1\) , \( i + 1\) , \( i + 1\) , \( -5 i\) , \( i - 1\bigr] \)
40000.3-g2	\( \bigl[i + 1\) , \( i - 1\) , \( 0\) , \( 124 i + 10\) , \( -401 i - 494\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph