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

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

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

Curve label	Weierstrass Coefficients
135.1-f1	\( \bigl[a\) , \( a + 1\) , \( a\) , \( 7 a - 15\) , \( -8 a + 30\bigr] \)
135.1-f2	\( \bigl[a\) , \( a + 1\) , \( a\) , \( -13 a + 5\) , \( -48 a + 178\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph