Properties

Base field \(\Q(\sqrt{197}) \)
Label 2.2.197.1-28.1-a
Conductor 28.1
Rank bounds 0...1

Related objects

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Base field \(\Q(\sqrt{197}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 49 \); class number \(1\).

Elliptic curves in class 28.1-a over \(\Q(\sqrt{197}) \)

Isogeny class 28.1-a contains only one elliptic curve.

Curve label Weierstrass Coefficients
28.1-a1 \( \bigl[a + 1\) , \( a + 1\) , \( 1\) , \( -80 a + 834\) , \( -4565 a + 35020\bigr] \)

Rank

Rank \(r\) satisfies \(0 \le r \le 1\)

Isogeny matrix

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

Isogeny graph