Elliptic curve isogeny class 12.2-a over number field \(\Q(\sqrt{10}) \)

• Base field: \(\Q(\sqrt{10}) \)
• Label: 2.2.40.1-12.2-a
• Conductor: 12.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 12.2-a over \(\Q(\sqrt{10}) \)

Isogeny class 12.2-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label	Weierstrass Coefficients
12.2-a1	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 202 a + 638\) , \( 1306 a + 4130\bigr] \)
12.2-a2	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -58 a - 182\) , \( 294 a + 930\bigr] \)
12.2-a3	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -28 a - 87\) , \( -107 a - 338\bigr] \)
12.2-a4	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -798 a - 2522\) , \( 22946 a + 72562\bigr] \)

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