Properties

Base field \(\Q(\sqrt{-3}) \)
Label 2.0.3.1-86700.1-b
Conductor 86700.1
Rank \( 0 \)

Related objects

Learn more about

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

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

Elliptic curves in class 86700.1-b over \(\Q(\sqrt{-3}) \)

Isogeny class 86700.1-b contains 8 curves linked by isogenies of degrees dividing 16.

Curve label Weierstrass Coefficients
86700.1-b1 \( \bigl[a + 1\) , \( a\) , \( 0\) , \( -79 a + 79\) , \( 385\bigr] \)
86700.1-b2 \( \bigl[a + 1\) , \( a\) , \( 0\) , \( 6551 a - 6551\) , \( -968765\bigr] \)
86700.1-b3 \( \bigl[a + 1\) , \( a\) , \( 0\) , \( 3061 a - 3061\) , \( 99645\bigr] \)
86700.1-b4 \( \bigl[a + 1\) , \( a\) , \( 0\) , \( -1439 a + 1439\) , \( 17745\bigr] \)
86700.1-b5 \( \bigl[a + 1\) , \( a\) , \( 0\) , \( -7219 a + 7219\) , \( -216923\bigr] \)
86700.1-b6 \( \bigl[a + 1\) , \( a\) , \( 0\) , \( -1359 a + 1359\) , \( 20097\bigr] \)
86700.1-b7 \( \bigl[a + 1\) , \( a\) , \( 0\) , \( -113469 a + 113469\) , \( -14645673\bigr] \)
86700.1-b8 \( \bigl[a + 1\) , \( a\) , \( 0\) , \( -21759 a + 21759\) , \( 1248177\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 16 & 8 & 4 & 8 & 2 & 16 & 4 \\ 16 & 1 & 8 & 4 & 2 & 8 & 4 & 16 \\ 8 & 8 & 1 & 2 & 4 & 4 & 8 & 8 \\ 4 & 4 & 2 & 1 & 2 & 2 & 4 & 4 \\ 8 & 2 & 4 & 2 & 1 & 4 & 2 & 8 \\ 2 & 8 & 4 & 2 & 4 & 1 & 8 & 2 \\ 16 & 4 & 8 & 4 & 2 & 8 & 1 & 16 \\ 4 & 16 & 8 & 4 & 8 & 2 & 16 & 1 \end{array}\right)\)

Isogeny graph