Elliptic curve isogeny class 90000.3-v over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-90000.3-v
• Conductor: 90000.3
• Rank: \( 1 \)

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

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

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 5 & 10 \\ 2 & 1 & 10 & 5 \\ 5 & 10 & 1 & 2 \\ 10 & 5 & 2 & 1 \end{array}\right)\)

Isogeny graph

Elliptic curves in class 90000.3-v over \(\Q(\sqrt{-1}) \)

Isogeny class 90000.3-v contains 4 curves linked by isogenies of degrees dividing 10.

Curve label	Weierstrass Coefficients
90000.3-v1	\( \bigl[i + 1\) , \( i - 1\) , \( i + 1\) , \( 1333 i + 280\) , \( -9224 i - 18839\bigr] \)
90000.3-v2	\( \bigl[i + 1\) , \( i - 1\) , \( i + 1\) , \( 133 i - 120\) , \( 776 i - 839\bigr] \)
90000.3-v3	\( \bigl[i + 1\) , \( -i\) , \( 0\) , \( 85 i + 197\) , \( -284 i + 9285\bigr] \)
90000.3-v4	\( \bigl[i + 1\) , \( -i\) , \( 0\) , \( 385 i + 297\) , \( -884 i + 4085\bigr] \)