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

• Base field: \(\Q(\sqrt{10}) \)
• Label: 2.2.40.1-135.1-h
• Conductor: 135.1
• Rank: \( 0 \)

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

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

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

Isogeny class 135.1-h contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
135.1-h1	\( \bigl[a\) , \( -a\) , \( 0\) , \( -7 a + 22\) , \( 154 a - 487\bigr] \)
135.1-h2	\( \bigl[a\) , \( -a\) , \( 0\) , \( 213 a - 678\) , \( 3366 a - 10647\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph