Elliptic curve isogeny class 135.4-e over number field \(\Q(\sqrt{10}) \)

• Base field: \(\Q(\sqrt{10}) \)
• Label: 2.2.40.1-135.4-e
• Conductor: 135.4
• Rank: \( 1 \)

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

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

Elliptic curves in class 135.4-e over \(\Q(\sqrt{10}) \)

Isogeny class 135.4-e contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
135.4-e1	\( \bigl[0\) , \( a + 1\) , \( a + 1\) , \( 2 a - 1\) , \( -a + 1\bigr] \)
135.4-e2	\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 6 a + 9\) , \( 7 a + 15\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph