Elliptic curve isogeny class 135.1-b over number field \(\Q(\sqrt{10}) \)

• Base field: \(\Q(\sqrt{10}) \)
• Label: 2.2.40.1-135.1-b
• Conductor: 135.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 135.1-b over \(\Q(\sqrt{10}) \)

Isogeny class 135.1-b contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
135.1-b1	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 304 a - 970\) , \( 5610 a - 17760\bigr] \)
135.1-b2	\( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 4 a - 10\) , \( 10 a - 32\bigr] \)
135.1-b3	\( \bigl[a\) , \( -a\) , \( 1\) , \( -2\) , \( 0\bigr] \)
135.1-b4	\( \bigl[a\) , \( -a\) , \( 1\) , \( 15 a - 62\) , \( 113 a - 373\bigr] \)

Rank

Rank: \( 1 \)

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