Properties

Base field \(\Q(\sqrt{37}) \)
Label 2.2.37.1-324.1-s
Conductor 324.1
Rank \( 1 \)

Related objects

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Base field \(\Q(\sqrt{37}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 9 \); class number \(1\).

Elliptic curves in class 324.1-s over \(\Q(\sqrt{37}) \)

Isogeny class 324.1-s contains 2 curves linked by isogenies of degree 3.

Curve label Weierstrass Coefficients
324.1-s1 \( \bigl[a\) , \( -a\) , \( 1\) , \( -176 a + 621\) , \( 3105 a - 10996\bigr] \)
324.1-s2 \( \bigl[a\) , \( -a\) , \( 0\) , \( 6 a + 21\) , \( 383 a + 976\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph