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

• Base field: \(\Q(\sqrt{-10}) \)
• Label: 2.0.40.1-405.1-a
• Conductor: 405.1
• Rank: \( 0 \)

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

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

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

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

Curve label	Weierstrass Coefficients
405.1-a1	\( \bigl[a\) , \( 1\) , \( a\) , \( -3955\) , \( -178157\bigr] \)
405.1-a2	\( \bigl[a\) , \( 1\) , \( a\) , \( 5\) , \( 43\bigr] \)
405.1-a3	\( \bigl[a\) , \( 1\) , \( a\) , \( 1265\) , \( -9785\bigr] \)
405.1-a4	\( \bigl[a\) , \( 1\) , \( a\) , \( -355\) , \( -1037\bigr] \)
405.1-a5	\( \bigl[a\) , \( 1\) , \( a\) , \( -175\) , \( 1015\bigr] \)
405.1-a6	\( \bigl[a\) , \( 1\) , \( a\) , \( -4855\) , \( -127937\bigr] \)
405.1-a7	\( \bigl[a\) , \( 1\) , \( a\) , \( -2875\) , \( 60955\bigr] \)
405.1-a8	\( \bigl[a\) , \( 1\) , \( a\) , \( -77755\) , \( -8307317\bigr] \)

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