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

• Base field: \(\Q(\sqrt{-10}) \)
• Label: 2.0.40.1-720.1-c
• Conductor: 720.1
• Rank: \( 0 \)

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

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

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

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

Curve label	Weierstrass Coefficients
720.1-c1	\( \bigl[a\) , \( -1\) , \( 0\) , \( -436\) , \( -6160\bigr] \)
720.1-c2	\( \bigl[a\) , \( -1\) , \( 0\) , \( 4\) , \( 0\bigr] \)
720.1-c3	\( \bigl[a\) , \( -1\) , \( 0\) , \( 144\) , \( -504\bigr] \)
720.1-c4	\( \bigl[a\) , \( -1\) , \( 0\) , \( -36\) , \( 0\bigr] \)
720.1-c5	\( \bigl[a\) , \( -1\) , \( 0\) , \( -16\) , \( 56\bigr] \)
720.1-c6	\( \bigl[a\) , \( -1\) , \( 0\) , \( -536\) , \( -4200\bigr] \)
720.1-c7	\( \bigl[a\) , \( -1\) , \( 0\) , \( -316\) , \( 2576\bigr] \)
720.1-c8	\( \bigl[a\) , \( -1\) , \( 0\) , \( -8636\) , \( -299040\bigr] \)

Rank

Rank: \( 0 \)

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