Properties

Base field 3.3.733.1
Label 3.3.733.1-8.2-b
Conductor 8.2
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 8.2-b over 3.3.733.1

Isogeny class 8.2-b contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
8.2-b1 \( \bigl[a^{2} - 4\) , \( -a^{2} + a + 4\) , \( a^{2} + a - 4\) , \( 9 a^{2} + 2 a - 67\) , \( -8 a^{2} - 2 a + 50\bigr] \)
8.2-b2 \( \bigl[a^{2} + a - 4\) , \( a^{2} - a - 4\) , \( a^{2} - 4\) , \( -2 a^{2} + 10 a - 7\) , \( -13 a^{2} + 55 a - 50\bigr] \)

Rank

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Isogeny matrix

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph