Properties

Base field \(\Q(\sqrt{19}) \)
Label 2.2.76.1-171.1-a
Conductor 171.1
Rank \( 1 \)

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

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

Elliptic curves in class 171.1-a over \(\Q(\sqrt{19}) \)

Isogeny class 171.1-a contains only one elliptic curve.

Curve label Weierstrass Coefficients
171.1-a1 \( \bigl[1\) , \( 1\) , \( a\) , \( -659572 a - 2875005\) , \( 608482693 a + 2652314563\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph