Elliptic curve isogeny class 45.1-e over number field \(\Q(\sqrt{10}) \)

• Base field: \(\Q(\sqrt{10}) \)
• Label: 2.2.40.1-45.1-e
• Conductor: 45.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 45.1-e over \(\Q(\sqrt{10}) \)

Isogeny class 45.1-e contains 8 curves linked by isogenies of degrees dividing 16.

Curve label	Weierstrass Coefficients
45.1-e1	\( \bigl[a\) , \( 0\) , \( 0\) , \( -438\) , \( -7038\bigr] \)
45.1-e2	\( \bigl[a\) , \( 0\) , \( 0\) , \( 2\) , \( 2\bigr] \)
45.1-e3	\( \bigl[a\) , \( 0\) , \( 0\) , \( 142\) , \( -222\bigr] \)
45.1-e4	\( \bigl[a\) , \( 0\) , \( 0\) , \( -38\) , \( -78\bigr] \)
45.1-e5	\( \bigl[a\) , \( 0\) , \( 0\) , \( -18\) , \( 18\bigr] \)
45.1-e6	\( \bigl[a\) , \( 0\) , \( 0\) , \( -538\) , \( -5278\bigr] \)
45.1-e7	\( \bigl[a\) , \( 0\) , \( 0\) , \( -318\) , \( 1938\bigr] \)
45.1-e8	\( \bigl[a\) , \( 0\) , \( 0\) , \( -8638\) , \( -316318\bigr] \)

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