Elliptic curve isogeny class 490.1-a over number field \(\Q(\sqrt{10}) \)

• Base field: \(\Q(\sqrt{10}) \)
• Label: 2.2.40.1-490.1-a
• Conductor: 490.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 490.1-a over \(\Q(\sqrt{10}) \)

Isogeny class 490.1-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
490.1-a1	\( \bigl[a\) , \( -1\) , \( a\) , \( 5\) , \( -15\bigr] \)
490.1-a2	\( \bigl[a\) , \( -1\) , \( a\) , \( -75\) , \( -223\bigr] \)
490.1-a3	\( \bigl[a\) , \( -1\) , \( a\) , \( -355\) , \( 2185\bigr] \)
490.1-a4	\( \bigl[a\) , \( -1\) , \( a\) , \( -1075\) , \( -14023\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph