Elliptic curve isogeny class 10000.3-f over number field \(\Q(\sqrt{-1}) \)

• Base field: \(\Q(\sqrt{-1}) \)
• Label: 2.0.4.1-10000.3-f
• Conductor: 10000.3
• Rank: \( 0 \)

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

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

Elliptic curves in class 10000.3-f over \(\Q(\sqrt{-1}) \)

Isogeny class 10000.3-f contains 4 curves linked by isogenies of degrees dividing 15.

Curve label	Weierstrass Coefficients
10000.3-f1	\( \bigl[i + 1\) , \( 1\) , \( 0\) , \( -2008 i - 1506\) , \( -48554 i - 8828\bigr] \)
10000.3-f2	\( \bigl[i + 1\) , \( -i + 1\) , \( i + 1\) , \( 47 i - 36\) , \( 236 i - 43\bigr] \)
10000.3-f3	\( \bigl[i + 1\) , \( 1\) , \( 0\) , \( -8 i - 6\) , \( -154 i - 28\bigr] \)
10000.3-f4	\( \bigl[i + 1\) , \( -i + 1\) , \( i + 1\) , \( -353 i + 264\) , \( -1744 i + 317\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 15 & 3 & 5 \\ 15 & 1 & 5 & 3 \\ 3 & 5 & 1 & 15 \\ 5 & 3 & 15 & 1 \end{array}\right)\)

Isogeny graph