Properties

Base field 3.3.49.1
Label 3.3.49.1-56.1-a
Conductor 56.1
Rank not recorded

Related objects

Learn more about

Base field 3.3.49.1

Generator \(a\), with minimal polynomial \( x^{3} - x^{2} - 2 x + 1 \); class number \(1\).

Elliptic curves in class 56.1-a over 3.3.49.1

Isogeny class 56.1-a contains 6 curves linked by isogenies of degrees dividing 18.

Curve label Weierstrass Coefficients
56.1-a1 \( \bigl[1\) , \( 0\) , \( 1\) , \( -2731\) , \( -55146\bigr] \)
56.1-a2 \( \bigl[1\) , \( 0\) , \( 1\) , \( -171\) , \( -874\bigr] \)
56.1-a3 \( \bigl[1\) , \( 0\) , \( 1\) , \( -36\) , \( -70\bigr] \)
56.1-a4 \( \bigl[1\) , \( 0\) , \( 1\) , \( -11\) , \( 12\bigr] \)
56.1-a5 \( \bigl[1\) , \( 0\) , \( 1\) , \( -1\) , \( 0\bigr] \)
56.1-a6 \( \bigl[1\) , \( 0\) , \( 1\) , \( 4\) , \( -6\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

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

Isogeny graph