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

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-40000.3-h
• Conductor: 40000.3
• Rank: \( 0 \)

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

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

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

Isogeny class 40000.3-h contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
40000.3-h1	\( \bigl[i + 1\) , \( -i - 1\) , \( i + 1\) , \( 666 i - 331\) , \( 7616 i + 953\bigr] \)
40000.3-h2	\( \bigl[i + 1\) , \( -i + 1\) , \( i + 1\) , \( -668 i - 331\) , \( 7616 i - 953\bigr] \)
40000.3-h3	\( \bigl[0\) , \( -i + 1\) , \( 0\) , \( 166 i + 75\) , \( 49 i + 1099\bigr] \)
40000.3-h4	\( \bigl[0\) , \( i + 1\) , \( 0\) , \( -166 i + 75\) , \( -49 i + 1099\bigr] \)
40000.3-h5	\( \bigl[i + 1\) , \( -i - 1\) , \( 0\) , \( -83 i - 81\) , \( 679 i + 453\bigr] \)
40000.3-h6	\( \bigl[i + 1\) , \( -1\) , \( 0\) , \( 83 i - 81\) , \( -679 i + 453\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 4 & 8 \\ 8 & 1 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 2 & 4 & 2 \\ 2 & 4 & 2 & 1 & 2 & 4 \\ 4 & 8 & 4 & 2 & 1 & 8 \\ 8 & 4 & 2 & 4 & 8 & 1 \end{array}\right)\)

Isogeny graph