Elliptic curve isogeny class 36.2-a over number field \(\Q(\sqrt{10}) \)

• Base field: \(\Q(\sqrt{10}) \)
• Label: 2.2.40.1-36.2-a
• Conductor: 36.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 36.2-a over \(\Q(\sqrt{10}) \)

Isogeny class 36.2-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
36.2-a1	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -2770 a - 8758\) , \( -17622 a - 55726\bigr] \)
36.2-a2	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -210 a - 663\) , \( 2415 a + 7637\bigr] \)
36.2-a3	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -2000 a - 6323\) , \( -89209 a - 282104\bigr] \)
36.2-a4	\( \bigl[a\) , \( a\) , \( a\) , \( -204 a - 650\) , \( 2468 a + 7802\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 6 & 2 & 3 \\ 6 & 1 & 3 & 2 \\ 2 & 3 & 1 & 6 \\ 3 & 2 & 6 & 1 \end{array}\right)\)

Isogeny graph