Properties

Base field \(\Q(\sqrt{19}) \)
Label 2.2.76.1-72.1-f
Conductor 72.1
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 72.1-f over \(\Q(\sqrt{19}) \)

Isogeny class 72.1-f contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
72.1-f1 \( \bigl[a + 1\) , \( a\) , \( 0\) , \( 3092 a + 13478\) , \( -69546 a - 303144\bigr] \)
72.1-f2 \( \bigl[a + 1\) , \( a\) , \( 0\) , \( -838 a - 3652\) , \( -13842 a - 60336\bigr] \)
72.1-f3 \( \bigl[a + 1\) , \( a\) , \( 0\) , \( -448 a - 1952\) , \( 9106 a + 39692\bigr] \)
72.1-f4 \( \bigl[a + 1\) , \( a\) , \( 0\) , \( -11008 a - 47982\) , \( -1354810 a - 5905480\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph