Elliptic curve isogeny class 405.1-e over number field \(\Q(\sqrt{10}) \)

• Base field: \(\Q(\sqrt{10}) \)
• Label: 2.2.40.1-405.1-e
• Conductor: 405.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 405.1-e over \(\Q(\sqrt{10}) \)

Isogeny class 405.1-e contains 8 curves linked by isogenies of degrees dividing 16.

Curve label	Weierstrass Coefficients
405.1-e1	\( \bigl[a\) , \( -1\) , \( a\) , \( -3965\) , \( 178157\bigr] \)
405.1-e2	\( \bigl[a\) , \( -1\) , \( a\) , \( -5\) , \( -43\bigr] \)
405.1-e3	\( \bigl[a\) , \( -1\) , \( a\) , \( 1255\) , \( 9785\bigr] \)
405.1-e4	\( \bigl[a\) , \( -1\) , \( a\) , \( -365\) , \( 1037\bigr] \)
405.1-e5	\( \bigl[a\) , \( -1\) , \( a\) , \( -185\) , \( -1015\bigr] \)
405.1-e6	\( \bigl[a\) , \( -1\) , \( a\) , \( -4865\) , \( 127937\bigr] \)
405.1-e7	\( \bigl[a\) , \( -1\) , \( a\) , \( -2885\) , \( -60955\bigr] \)
405.1-e8	\( \bigl[a\) , \( -1\) , \( a\) , \( -77765\) , \( 8307317\bigr] \)

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