Elliptic curve isogeny class 135.2-b over number field \(\Q(\sqrt{10}) \)

• Base field: \(\Q(\sqrt{10}) \)
• Label: 2.2.40.1-135.2-b
• Conductor: 135.2
• Rank: \( 1 \)

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

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

Elliptic curves in class 135.2-b over \(\Q(\sqrt{10}) \)

Isogeny class 135.2-b contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
135.2-b1	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -4 a - 10\) , \( -10 a - 32\bigr] \)
135.2-b2	\( \bigl[a\) , \( a\) , \( 1\) , \( -16 a - 62\) , \( -113 a - 373\bigr] \)
135.2-b3	\( \bigl[a\) , \( a\) , \( 1\) , \( -a - 2\) , \( 0\bigr] \)
135.2-b4	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( -304 a - 970\) , \( -5610 a - 17760\bigr] \)

Rank

Rank: \( 1 \)

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