Properties

Base field \(\Q(\sqrt{-3}) \)
Label 2.0.3.1-102675.3-a
Conductor 102675.3
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 102675.3-a over \(\Q(\sqrt{-3}) \)

Isogeny class 102675.3-a contains 8 curves linked by isogenies of degrees dividing 16.

Curve label Weierstrass Coefficients
102675.3-a1 \( \bigl[1\) , \( -a\) , \( 0\) , \( 4401 a - 3631\) , \( -210053 a + 60377\bigr] \)
102675.3-a2 \( \bigl[1\) , \( -a\) , \( 0\) , \( a - 1\) , \( 47 a - 13\bigr] \)
102675.3-a3 \( \bigl[1\) , \( -a\) , \( 0\) , \( -1399 a + 1154\) , \( -10719 a + 2640\bigr] \)
102675.3-a4 \( \bigl[1\) , \( -a\) , \( 0\) , \( 401 a - 331\) , \( -1413 a + 507\bigr] \)
102675.3-a5 \( \bigl[1\) , \( -a\) , \( 0\) , \( 201 a - 166\) , \( 1081 a - 250\bigr] \)
102675.3-a6 \( \bigl[1\) , \( -a\) , \( 0\) , \( 5401 a - 4456\) , \( -151963 a + 44282\bigr] \)
102675.3-a7 \( \bigl[1\) , \( -a\) , \( 0\) , \( 3201 a - 2641\) , \( 69511 a - 18715\bigr] \)
102675.3-a8 \( \bigl[1\) , \( -a\) , \( 0\) , \( 86401 a - 71281\) , \( -9735073 a + 2766287\bigr] \)

Rank

Rank: \( 1 \)

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