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

• Base field: \(\Q(\sqrt{10}) \)
• Label: 2.2.40.1-135.1-g
• 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-g over \(\Q(\sqrt{10}) \)

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

Curve label	Weierstrass Coefficients
135.1-g1	\( \bigl[a\) , \( a + 1\) , \( a + 1\) , \( 78 a - 241\) , \( 657 a - 2080\bigr] \)
135.1-g2	\( \bigl[a\) , \( a + 1\) , \( a + 1\) , \( 3 a - 1\) , \( 2 a + 1\bigr] \)
135.1-g3	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 8 a - 26\) , \( -38 a + 120\bigr] \)
135.1-g4	\( \bigl[0\) , \( a - 1\) , \( 0\) , \( 68 a - 266\) , \( 506 a - 1784\bigr] \)

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