Properties

Base field 3.3.733.1
Label 3.3.733.1-7.1-b
Conductor 7.1
Rank not recorded

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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 7.1-b over 3.3.733.1

Isogeny class 7.1-b contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
7.1-b1 \( \bigl[a^{2} - 5\) , \( a^{2} - a - 5\) , \( 1\) , \( -572 a^{2} + 2121 a - 1723\) , \( -25034 a^{2} + 92549 a - 74316\bigr] \)
7.1-b2 \( \bigl[a^{2} - 5\) , \( a^{2} - a - 5\) , \( 1\) , \( 28 a^{2} + 141 a - 533\) , \( -38 a^{2} + 1741 a - 4144\bigr] \)
7.1-b3 \( \bigl[a^{2} - 5\) , \( a^{2} - a - 5\) , \( 1\) , \( -32 a^{2} + 131 a - 128\) , \( -442 a^{2} + 1653 a - 1360\bigr] \)
7.1-b4 \( \bigl[1\) , \( a^{2} - a - 5\) , \( a^{2} + a - 5\) , \( 274158 a^{2} + 416226 a - 870957\) , \( 116637957 a^{2} + 177079592 a - 370544096\bigr] \)
7.1-b5 \( \bigl[a + 1\) , \( a\) , \( 0\) , \( 248 a^{2} + 46 a - 1678\) , \( 3590 a^{2} + 641 a - 24373\bigr] \)
7.1-b6 \( \bigl[a + 1\) , \( -a^{2} + 4\) , \( a^{2} - 4\) , \( 454041244 a^{2} + 80907460 a - 3082964015\) , \( 1380930983897 a^{2} + 246073726249 a - 9376594279770\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

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

Isogeny graph