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

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

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

Curve label	Weierstrass Coefficients
135.2-e1	\( \bigl[a\) , \( -a + 1\) , \( 1\) , \( -15 a + 50\) , \( -7 a + 24\bigr] \)
135.2-e2	\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 56 a - 190\) , \( 242 a - 728\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph