Properties

Base field 3.3.733.1
Label 3.3.733.1-2.1-b
Conductor 2.1
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 2.1-b over 3.3.733.1

Isogeny class 2.1-b contains 4 curves linked by isogenies of degrees dividing 6.

Curve label Weierstrass Coefficients
2.1-b1 \( \bigl[a^{2} - 5\) , \( 0\) , \( a + 1\) , \( 18957864 a^{2} + 3380608 a - 128731016\) , \( 72417315372 a^{2} + 12904890246 a - 491718787736\bigr] \)
2.1-b2 \( \bigl[a^{2} - 5\) , \( 0\) , \( a + 1\) , \( 253164 a^{2} + 44843 a - 1718321\) , \( 82486459 a^{2} + 14678682 a - 560037260\bigr] \)
2.1-b3 \( \bigl[a^{2} - 5\) , \( -a^{2} + 5\) , \( 0\) , \( -121 a^{2} + 439 a - 338\) , \( -2195 a^{2} + 8115 a - 6516\bigr] \)
2.1-b4 \( \bigl[a^{2} - 5\) , \( -a^{2} + 5\) , \( 0\) , \( -11 a^{2} + 29 a - 3\) , \( 37 a^{2} - 146 a + 133\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

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

Isogeny graph