Properties

Base field \(\Q(\sqrt{65}) \)
Label 2.2.65.1-45.1-a
Conductor 45.1
Rank not recorded

Related objects

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Base field \(\Q(\sqrt{65}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 16 \); class number \(2\).

Elliptic curves in class 45.1-a over \(\Q(\sqrt{65}) \)

Isogeny class 45.1-a contains 8 curves linked by isogenies of degrees dividing 16.

Curve label Weierstrass Coefficients
45.1-a1 \( \bigl[a\) , \( a + 1\) , \( a\) , \( -986 a - 3512\) , \( -67741 a - 239296\bigr] \)
45.1-a2 \( \bigl[a\) , \( a + 1\) , \( a\) , \( 4 a + 8\) , \( 19 a + 64\bigr] \)
45.1-a3 \( \bigl[a\) , \( a + 1\) , \( a\) , \( 319 a + 1128\) , \( -2137 a - 7552\bigr] \)
45.1-a4 \( \bigl[a\) , \( a + 1\) , \( a\) , \( -86 a - 312\) , \( -751 a - 2656\bigr] \)
45.1-a5 \( \bigl[a\) , \( a + 1\) , \( a\) , \( -41 a - 152\) , \( 173 a + 608\bigr] \)
45.1-a6 \( \bigl[a\) , \( a + 1\) , \( a\) , \( -1211 a - 4312\) , \( -50801 a - 179456\bigr] \)
45.1-a7 \( \bigl[a\) , \( a + 1\) , \( a\) , \( -716 a - 2552\) , \( 18653 a + 65888\bigr] \)
45.1-a8 \( \bigl[a\) , \( a + 1\) , \( a\) , \( -19436 a - 69112\) , \( -3044561 a - 10754816\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 16 & 8 & 4 & 8 & 2 & 16 & 4 \\ 16 & 1 & 8 & 4 & 2 & 8 & 4 & 16 \\ 8 & 8 & 1 & 2 & 4 & 4 & 8 & 8 \\ 4 & 4 & 2 & 1 & 2 & 2 & 4 & 4 \\ 8 & 2 & 4 & 2 & 1 & 4 & 2 & 8 \\ 2 & 8 & 4 & 2 & 4 & 1 & 8 & 2 \\ 16 & 4 & 8 & 4 & 2 & 8 & 1 & 16 \\ 4 & 16 & 8 & 4 & 8 & 2 & 16 & 1 \end{array}\right)\)

Isogeny graph