Properties

Base field \(\Q(\sqrt{10}) \)
Label 2.2.40.1-18.2-d
Conductor 18.2
Rank \( 1 \)

Related objects

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

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

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

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

Curve label Weierstrass Coefficients
18.2-d1 \( \bigl[a\) , \( -a\) , \( a\) , \( 10 a - 39\) , \( -21 a + 66\bigr] \)
18.2-d2 \( \bigl[a\) , \( -a\) , \( a\) , \( -70 a + 221\) , \( -165 a + 526\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph