Properties

Base field 3.3.733.1
Label 3.3.733.1-2.1-c
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-c over 3.3.733.1

Isogeny class 2.1-c contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
2.1-c1 \( \bigl[a^{2} - 5\) , \( -a + 1\) , \( 1\) , \( -1022218105 a^{2} - 1551930198 a + 3247458136\) , \( 33252622286582 a^{2} + 50484087904678 a - 105639391507833\bigr] \)
2.1-c2 \( \bigl[a^{2} - 5\) , \( -a + 1\) , \( 1\) , \( -16355430935 a^{2} - 24830793973 a + 51959143466\) , \( 2128166401426176 a^{2} + 3230979462595240 a - 6760916529725773\bigr] \)
2.1-c3 \( \bigl[1\) , \( a\) , \( a^{2} - 4\) , \( 2520357667917543665449320 a^{2} + 3826403733269585827021303 a - 8006858771205877744474390\) , \( 11558975454636154624549965415411690476 a^{2} + 17548821500773715449595541137894110295 a - 36721408704494578039244986060014379468\bigr] \)
2.1-c4 \( \bigl[1\) , \( -a^{2} + 6\) , \( a\) , \( -3 a^{2} - 3 a + 15\) , \( a^{2} + 3 a - 1\bigr] \)
2.1-c5 \( \bigl[a + 1\) , \( -a + 1\) , \( a^{2} - 5\) , \( -44174316128285721 a^{2} - 67065389289594007 a + 140336236819129681\) , \( 8484866098384540422058642 a^{2} + 12881712674525578166721139 a - 26955350586605825705197871\bigr] \)
2.1-c6 \( \bigl[a + 1\) , \( -a + 1\) , \( a^{2} - 5\) , \( -168562107136250046 a^{2} - 255910771809962227 a + 535500577238303301\) , \( -61353841318711367560260837 a^{2} - 93147322088742339719223147 a + 194913423901376825030234481\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

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

Isogeny graph