Elliptic curve isogeny class 720.1-f over number field \(\Q(\sqrt{-10}) \)

• Base field: \(\Q(\sqrt{-10}) \)
• Label: 2.0.40.1-720.1-f
• Conductor: 720.1
• Rank: \( 1 \)

Base field \(\Q(\sqrt{-10}) \)

Generator \(a\), with minimal polynomial \( x^{2} + 10 \); class number \(2\).

Elliptic curves in class 720.1-f over \(\Q(\sqrt{-10}) \)

Isogeny class 720.1-f contains 8 curves linked by isogenies of degrees dividing 16.

Curve label	Weierstrass Coefficients
720.1-f1	\( \bigl[0\) , \( 1\) , \( 0\) , \( -1760\) , \( 52788\bigr] \)
720.1-f2	\( \bigl[0\) , \( 1\) , \( 0\) , \( 0\) , \( -12\bigr] \)
720.1-f3	\( \bigl[0\) , \( 1\) , \( 0\) , \( 560\) , \( 2900\bigr] \)
720.1-f4	\( \bigl[0\) , \( 1\) , \( 0\) , \( -160\) , \( 308\bigr] \)
720.1-f5	\( \bigl[0\) , \( 1\) , \( 0\) , \( -80\) , \( -300\bigr] \)
720.1-f6	\( \bigl[0\) , \( 1\) , \( 0\) , \( -2160\) , \( 37908\bigr] \)
720.1-f7	\( \bigl[0\) , \( 1\) , \( 0\) , \( -1280\) , \( -18060\bigr] \)
720.1-f8	\( \bigl[0\) , \( 1\) , \( 0\) , \( -34560\) , \( 2461428\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 16 & 8 & 4 & 8 & 2 & 16 & 4 \\ 16 & 1 & 8 & 4 & 2 & 8 & 4 & 16 \\ 8 & 8 & 1 & 2 & 4 & 4 & 8 & 8 \\ 4 & 4 & 2 & 1 & 2 & 2 & 4 & 4 \\ 8 & 2 & 4 & 2 & 1 & 4 & 2 & 8 \\ 2 & 8 & 4 & 2 & 4 & 1 & 8 & 2 \\ 16 & 4 & 8 & 4 & 2 & 8 & 1 & 16 \\ 4 & 16 & 8 & 4 & 8 & 2 & 16 & 1 \end{array}\right)\)

Isogeny graph