Properties

Base field \(\Q(\sqrt{10}) \)
Label 2.2.40.1-18.2-a
Conductor 18.2
Rank \( 0 \)

Related objects

Learn more

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

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

Elliptic curves in class 18.2-a over \(\Q(\sqrt{10}) \)

Isogeny class 18.2-a contains 2 curves linked by isogenies of degree 3.

Curve label Weierstrass Coefficients
18.2-a1 \( \bigl[1\) , \( a + 1\) , \( 0\) , \( -143 a - 451\) , \( 1462 a + 4623\bigr] \)
18.2-a2 \( \bigl[1\) , \( a + 1\) , \( 0\) , \( 257 a + 814\) , \( 8740 a + 27638\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph