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

• Base field: \(\Q(\sqrt{10}) \)
• Label: 2.2.40.1-135.2-a
• Conductor: 135.2
• Rank: \( 0 \)

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

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

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

Isogeny class 135.2-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
135.2-a1	\( \bigl[1\) , \( -a + 1\) , \( a\) , \( 8\) , \( -22 a - 69\bigr] \)
135.2-a2	\( \bigl[1\) , \( -a + 1\) , \( a\) , \( -55 a - 167\) , \( -336 a - 1064\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph