Properties

Base field \(\Q(\sqrt{53}) \)
Label 2.2.53.1-37.2-a
Conductor 37.2
Rank \( 0 \)

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Base field \(\Q(\sqrt{53}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 13 \); class number \(1\).

Elliptic curves in class 37.2-a over \(\Q(\sqrt{53}) \)

Isogeny class 37.2-a contains only one elliptic curve.

Curve label Weierstrass Coefficients
37.2-a1 \( \bigl[a + 1\) , \( a\) , \( 1\) , \( 6 a + 11\) , \( 3 a + 33\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{r} 1 \end{array}\right)\)

Isogeny graph