Properties

Base field \(\Q(\sqrt{41}) \)
Label 2.2.41.1-81.1-b
Conductor 81.1
Rank \( 0 \)

Related objects

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Base field \(\Q(\sqrt{41}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 10 \); class number \(1\).

Elliptic curves in class 81.1-b over \(\Q(\sqrt{41}) \)

Isogeny class 81.1-b contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
81.1-b1 \( \bigl[1\) , \( -1\) , \( 0\) , \( -3\) , \( 2 a + 4\bigr] \)
81.1-b2 \( \bigl[1\) , \( -1\) , \( 0\) , \( 360 a + 972\) , \( -270 a - 729\bigr] \)
81.1-b3 \( \bigl[1\) , \( -1\) , \( 0\) , \( -90 a - 243\) , \( 0\bigr] \)
81.1-b4 \( \bigl[1\) , \( -1\) , \( 0\) , \( 90 a - 333\) , \( 0\bigr] \)
81.1-b5 \( \bigl[1\) , \( -1\) , \( 0\) , \( -3\) , \( -2 a + 6\bigr] \)
81.1-b6 \( \bigl[1\) , \( -1\) , \( 0\) , \( -360 a + 1332\) , \( 270 a - 999\bigr] \)

Rank

Rank: \( 0 \)

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