Properties

Base field \(\Q(\sqrt{41}) \)
Label 2.2.41.1-4.1-a
Conductor 4.1
Rank \( 0 \)

Related objects

Learn more

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

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

Elliptic curves in class 4.1-a over \(\Q(\sqrt{41}) \)

Isogeny class 4.1-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label Weierstrass Coefficients
4.1-a1 \( \bigl[1\) , \( 1\) , \( 0\) , \( 635 a - 2350\) , \( 15849 a - 58666\bigr] \)
4.1-a2 \( \bigl[1\) , \( 1\) , \( 0\) , \( 15 a - 55\) , \( -17 a + 63\bigr] \)
4.1-a3 \( \bigl[1\) , \( 1\) , \( 0\) , \( -15 a - 40\) , \( 17 a + 46\bigr] \)
4.1-a4 \( \bigl[1\) , \( 1\) , \( 0\) , \( -635 a - 1715\) , \( -15849 a - 42817\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph