Properties

Base field \(\Q(\sqrt{-3}) \)
Label 2.0.3.1-12675.1-a
Conductor 12675.1
Rank \( 0 \)

Related objects

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

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

Elliptic curves in class 12675.1-a over \(\Q(\sqrt{-3}) \)

Isogeny class 12675.1-a contains 8 curves linked by isogenies of degrees dividing 16.

Curve label Weierstrass Coefficients
12675.1-a1 \( \bigl[1\) , \( a + 1\) , \( 1\) , \( -879 a + 1650\) , \( -30133 a - 13197\bigr] \)
12675.1-a2 \( \bigl[1\) , \( a + 1\) , \( 1\) , \( a\) , \( 7 a + 3\bigr] \)
12675.1-a3 \( \bigl[1\) , \( a + 1\) , \( 1\) , \( 281 a - 525\) , \( -1491 a - 1033\bigr] \)
12675.1-a4 \( \bigl[1\) , \( a + 1\) , \( 1\) , \( -79 a + 150\) , \( -213 a - 7\bigr] \)
12675.1-a5 \( \bigl[1\) , \( a + 1\) , \( 1\) , \( -39 a + 75\) , \( 149 a + 117\bigr] \)
12675.1-a6 \( \bigl[1\) , \( a + 1\) , \( 1\) , \( -1079 a + 2025\) , \( -21863 a - 9057\bigr] \)
12675.1-a7 \( \bigl[1\) , \( a + 1\) , \( 1\) , \( -639 a + 1200\) , \( 9839 a + 5397\bigr] \)
12675.1-a8 \( \bigl[1\) , \( a + 1\) , \( 1\) , \( -17279 a + 32400\) , \( -1393193 a - 637617\bigr] \)

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