Properties

Base field \(\Q(\sqrt{161}) \)
Label 2.2.161.1-28.1-e
Conductor 28.1
Rank not recorded

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Base field \(\Q(\sqrt{161}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 40 \); class number \(1\).

Elliptic curves in class 28.1-e over \(\Q(\sqrt{161}) \)

Isogeny class 28.1-e contains 6 curves linked by isogenies of degrees dividing 18.

Curve label Weierstrass Coefficients
28.1-e1 \( \bigl[1\) , \( a\) , \( a + 1\) , \( -7453261000 a - 43559009551\) , \( 884743726381089 a + 5170697824615794\bigr] \)
28.1-e2 \( \bigl[1\) , \( a\) , \( a + 1\) , \( -22765000 a - 133045221\) , \( -301470021617 a - 1761877861908\bigr] \)
28.1-e3 \( \bigl[1\) , \( -a + 1\) , \( a\) , \( -195779001 a + 1339968025\) , \( -6303992811223 a + 43146347205413\bigr] \)
28.1-e4 \( \bigl[1\) , \( -a + 1\) , \( a\) , \( 1552572999 a - 10626257935\) , \( -68746620820639 a + 470521724873581\bigr] \)
28.1-e5 \( \bigl[1\) , \( -a + 1\) , \( a\) , \( 459852999 a - 3147366710\) , \( 13512395687294 a - 92482738061398\bigr] \)
28.1-e6 \( \bigl[1\) , \( a\) , \( a + 1\) , \( -119347789000 a - 697502942991\) , \( 56529348060097057 a + 330373834055752050\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 9 & 3 & 6 & 18 & 2 \\ 9 & 1 & 3 & 6 & 2 & 18 \\ 3 & 3 & 1 & 2 & 6 & 6 \\ 6 & 6 & 2 & 1 & 3 & 3 \\ 18 & 2 & 6 & 3 & 1 & 9 \\ 2 & 18 & 6 & 3 & 9 & 1 \end{array}\right)\)

Isogeny graph