Properties

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

Isogeny class 72.1-j contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
72.1-j1 \( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -51932 a + 226389\) , \( -98430345 a + 429047963\bigr] \)
72.1-j2 \( \bigl[0\) , \( 1\) , \( 0\) , \( 1\) , \( 0\bigr] \)
72.1-j3 \( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 14368 a - 62606\) , \( 1448893 a - 6315542\bigr] \)
72.1-j4 \( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 80668 a - 351601\) , \( -24905977 a + 108562673\bigr] \)
72.1-j5 \( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 213268 a - 929591\) , \( 111735445 a - 487043477\bigr] \)
72.1-j6 \( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( 1274068 a - 5553511\) , \( -1635400609 a + 7128546023\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 8 & 4 \\ 8 & 1 & 2 & 4 & 4 & 8 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 2 & 4 & 2 & 1 & 4 & 2 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 8 & 4 & 2 & 8 & 1 \end{array}\right)\)

Isogeny graph