Properties

Base field \(\Q(\sqrt{19}) \)
Label 2.2.76.1-19.1-a
Conductor 19.1
Rank \( 0 \)

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 19.1-a over \(\Q(\sqrt{19}) \)

Isogeny class 19.1-a contains 3 curves linked by isogenies of degrees dividing 9.

Curve label Weierstrass Coefficients
19.1-a1 \( \bigl[0\) , \( -1\) , \( a\) , \( -769\) , \( 8465\bigr] \)
19.1-a2 \( \bigl[0\) , \( -1\) , \( a\) , \( -9\) , \( 10\bigr] \)
19.1-a3 \( \bigl[0\) , \( -1\) , \( a\) , \( 1\) , \( -5\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph