Properties

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

Related objects

Learn more

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

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

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

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

Curve label Weierstrass Coefficients
135.4-d1 \( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 6 a - 15\) , \( 5 a - 15\bigr] \)
135.4-d2 \( \bigl[0\) , \( -a - 1\) , \( 1\) , \( 2 a + 5\) , \( -a - 7\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph