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

• Base field: \(\Q(\sqrt{10}) \)
• Label: 2.2.40.1-135.2-g
• 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-g over \(\Q(\sqrt{10}) \)

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

Curve label	Weierstrass Coefficients
135.2-g1	\( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( -4 a - 1\) , \( -3 a + 1\bigr] \)
135.2-g2	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -68 a - 266\) , \( -506 a - 1784\bigr] \)
135.2-g3	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( -8 a - 26\) , \( 38 a + 120\bigr] \)
135.2-g4	\( \bigl[a\) , \( -a + 1\) , \( a + 1\) , \( -79 a - 241\) , \( -658 a - 2080\bigr] \)

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