Properties

Base field \(\Q(\sqrt{-3}) \)
Label 2.0.3.1-87808.3-c
Conductor 87808.3
Rank \( 1 \)

Related objects

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

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

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

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

Curve label Weierstrass Coefficients
87808.3-c1 \( \bigl[0\) , \( 1\) , \( 0\) , \( 8185 a + 13642\) , \( 992919 a - 1040654\bigr] \)
87808.3-c2 \( \bigl[0\) , \( 1\) , \( 0\) , \( 25 a + 42\) , \( -329 a + 370\bigr] \)
87808.3-c3 \( \bigl[0\) , \( 1\) , \( 0\) , \( -215 a - 358\) , \( 6983 a - 7566\bigr] \)
87808.3-c4 \( \bigl[0\) , \( 1\) , \( 0\) , \( 1705 a + 2842\) , \( 77511 a - 80270\bigr] \)
87808.3-c5 \( \bigl[0\) , \( 1\) , \( 0\) , \( 9545 a - 44198\) , \( 852103 a - 3180206\bigr] \)
87808.3-c6 \( \bigl[0\) , \( 1\) , \( 0\) , \( -38295 a - 3718\) , \( 3218023 a - 1142126\bigr] \)
87808.3-c7 \( \bigl[0\) , \( 1\) , \( 0\) , \( 505 a + 842\) , \( -14953 a + 16242\bigr] \)
87808.3-c8 \( \bigl[0\) , \( 1\) , \( 0\) , \( 8745 a - 42918\) , \( 995719 a - 3381454\bigr] \)
87808.3-c9 \( \bigl[0\) , \( 1\) , \( 0\) , \( -37015 a - 4198\) , \( 3414599 a - 1299534\bigr] \)
87808.3-c10 \( \bigl[0\) , \( 1\) , \( 0\) , \( 131065 a + 218442\) , \( 63309463 a - 66707726\bigr] \)

Rank

Rank: \( 1 \)

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