Properties

Base field \(\Q(\sqrt{19}) \)
Label 2.2.76.1-81.1-a
Conductor 81.1
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 81.1-a over \(\Q(\sqrt{19}) \)

Isogeny class 81.1-a contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
81.1-a1 \( \bigl[a\) , \( -1\) , \( a + 1\) , \( 250441 a - 1091654\) , \( -138692376 a + 604546046\bigr] \)
81.1-a2 \( \bigl[a\) , \( -1\) , \( a + 1\) , \( 36286 a - 158174\) , \( 4799016 a - 20918431\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph