Properties

Base field \(\Q(\sqrt{19}) \)
Label 2.2.76.1-9.2-b
Conductor 9.2
Rank \( 1 \)

Related objects

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Base field \(\Q(\sqrt{19}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 19 \); class number \(1\).

Elliptic curves in class 9.2-b over \(\Q(\sqrt{19}) \)

Isogeny class 9.2-b contains only one elliptic curve.

Curve label Weierstrass Coefficients
9.2-b1 \( \bigl[0\) , \( 0\) , \( a\) , \( -4759 a + 20744\) , \( 231623 a - 1009626\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph