Properties

Base field 3.3.733.1
Label 3.3.733.1-14.1-a
Conductor 14.1
Rank not recorded

Related objects

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Base field 3.3.733.1

Generator \(a\), with minimal polynomial \( x^{3} - x^{2} - 7 x + 8 \); class number \(1\).

Elliptic curves in class 14.1-a over 3.3.733.1

Isogeny class 14.1-a contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
14.1-a1 \( \bigl[a + 1\) , \( a^{2} - a - 6\) , \( a\) , \( 12659494600 a^{2} + 2255846982 a - 85958636601\) , \( 1249197047855543 a^{2} + 222599518707425 a - 8482113899832843\bigr] \)
14.1-a2 \( \bigl[a + 1\) , \( a^{2} - a - 6\) , \( a\) , \( 800045825 a^{2} + 142563442 a - 5432353421\) , \( 19059955059430 a^{2} + 3396371157117 a - 129418101025383\bigr] \)
14.1-a3 \( \bigl[a + 1\) , \( a^{2} - a - 6\) , \( a\) , \( 135425830 a^{2} + 24132082 a - 919548541\) , \( -991007863993 a^{2} - 176591734617 a + 6728995711641\bigr] \)
14.1-a4 \( \bigl[a + 1\) , \( a^{2} - a - 6\) , \( a\) , \( -425483030 a^{2} - 75818338 a + 2889051679\) , \( 72233447083969 a^{2} + 12871572653085 a - 490468918899299\bigr] \)
14.1-a5 \( \bigl[a + 1\) , \( a^{2} - 5\) , \( a^{2} + a - 5\) , \( 2727719912262131 a^{2} + 486063540319786 a - 18521362200115984\) , \( -124929064793722765572661 a^{2} - 22261619768770883846309 a + 848274944932820465801609\bigr] \)
14.1-a6 \( \bigl[a + 1\) , \( -a^{2} - a + 4\) , \( a\) , \( -17 a^{2} - 3 a + 112\) , \( -78 a^{2} - 14 a + 528\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

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

Isogeny graph