Properties

Base field \(\Q(\sqrt{19}) \)
Label 2.2.76.1-72.1-a
Conductor 72.1
Rank not recorded

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

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

Curve label Weierstrass Coefficients
72.1-a1 \( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( -51931 a + 226392\) , \( 98500930 a - 429355550\bigr] \)
72.1-a2 \( \bigl[0\) , \( -1\) , \( 0\) , \( 1\) , \( 0\bigr] \)
72.1-a3 \( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( 14369 a - 62603\) , \( -1468403 a + 6400670\bigr] \)
72.1-a4 \( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( 80669 a - 351598\) , \( 24796372 a - 108084830\bigr] \)
72.1-a5 \( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( 213269 a - 929588\) , \( -112025240 a + 488306750\bigr] \)
72.1-a6 \( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( 1274069 a - 5553508\) , \( 1633669294 a - 7120999310\bigr] \)

Rank

Rank not yet determined.

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