Properties

Base field \(\Q(\sqrt{-3}) \)
Label 2.0.3.1-87808.3-t
Conductor 87808.3
Rank \( 0 \)

Related objects

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Base field \(\Q(\sqrt{-3}) \)

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

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrrrr} 1 & 9 & 3 & 6 & 18 & 18 & 18 & 9 & 9 & 2 \\ 9 & 1 & 3 & 6 & 18 & 18 & 2 & 9 & 9 & 18 \\ 3 & 3 & 1 & 2 & 6 & 6 & 6 & 3 & 3 & 6 \\ 6 & 6 & 2 & 1 & 3 & 3 & 3 & 6 & 6 & 3 \\ 18 & 18 & 6 & 3 & 1 & 9 & 9 & 2 & 18 & 9 \\ 18 & 18 & 6 & 3 & 9 & 1 & 9 & 18 & 2 & 9 \\ 18 & 2 & 6 & 3 & 9 & 9 & 1 & 18 & 18 & 9 \\ 9 & 9 & 3 & 6 & 2 & 18 & 18 & 1 & 9 & 18 \\ 9 & 9 & 3 & 6 & 18 & 2 & 18 & 9 & 1 & 18 \\ 2 & 18 & 6 & 3 & 9 & 9 & 9 & 18 & 18 & 1 \end{array}\right)\)

Isogeny graph

Elliptic curves in class 87808.3-t over \(\Q(\sqrt{-3}) \)

Isogeny class 87808.3-t contains 10 curves linked by isogenies of degrees dividing 18.

Curve label Weierstrass Coefficients
87808.3-t1 \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -21827 a + 8185\) , \( -992919 a + 1040654\bigr] \)
87808.3-t2 \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -67 a + 25\) , \( 329 a - 370\bigr] \)
87808.3-t3 \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 573 a - 215\) , \( -6983 a + 7566\bigr] \)
87808.3-t4 \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -4547 a + 1705\) , \( -77511 a + 80270\bigr] \)
87808.3-t5 \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 34653 a + 9545\) , \( -852103 a + 3180206\bigr] \)
87808.3-t6 \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 42013 a - 38295\) , \( -3218023 a + 1142126\bigr] \)
87808.3-t7 \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -1347 a + 505\) , \( 14953 a - 16242\bigr] \)
87808.3-t8 \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 34173 a + 8745\) , \( -995719 a + 3381454\bigr] \)
87808.3-t9 \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( 41213 a - 37015\) , \( -3414599 a + 1299534\bigr] \)
87808.3-t10 \( \bigl[0\) , \( -a + 1\) , \( 0\) , \( -349507 a + 131065\) , \( -63309463 a + 66707726\bigr] \)