Elliptic curve isogeny class 108.2-b over number field \(\Q(\sqrt{10}) \)

• Base field: \(\Q(\sqrt{10}) \)
• Label: 2.2.40.1-108.2-b
• Conductor: 108.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 108.2-b over \(\Q(\sqrt{10}) \)

Isogeny class 108.2-b contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
108.2-b1	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -46 a - 38\) , \( -178 a - 306\bigr] \)
108.2-b2	\( \bigl[a\) , \( -a\) , \( 0\) , \( 78 a + 255\) , \( -214 a - 673\bigr] \)
108.2-b3	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -326 a - 1063\) , \( -1367 a - 4283\bigr] \)
108.2-b4	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -26 a - 103\) , \( -131 a - 434\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph