Properties

Base field \(\Q(\sqrt{3}) \)
Label 2.2.12.1-2028.1-a
Conductor 2028.1
Rank \( 0 \)

Related objects

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

Generator \(a\), with minimal polynomial \( x^{2} - 3 \); class number \(1\).

Elliptic curves in class 2028.1-a over \(\Q(\sqrt{3}) \)

Isogeny class 2028.1-a contains 8 curves linked by isogenies of degrees dividing 12.

Curve label Weierstrass Coefficients
2028.1-a1 \( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 2382 a - 4131\) , \( -81893 a + 141844\bigr] \)
2028.1-a2 \( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 2512 a - 4341\) , \( -72563 a + 125602\bigr] \)
2028.1-a3 \( \bigl[0\) , \( 1\) , \( 0\) , \( -13\) , \( -4\bigr] \)
2028.1-a4 \( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -778 a + 1299\) , \( 61597 a - 106598\bigr] \)
2028.1-a5 \( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 747 a - 1311\) , \( 14182 a - 24584\bigr] \)
2028.1-a6 \( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 147 a - 261\) , \( -1208 a + 2092\bigr] \)
2028.1-a7 \( \bigl[0\) , \( 1\) , \( 0\) , \( -733\) , \( -7888\bigr] \)
2028.1-a8 \( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( 72 a - 171\) , \( -2333 a + 4144\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 3 & 4 & 12 & 6 & 2 & 12 & 4 \\ 3 & 1 & 12 & 4 & 2 & 6 & 4 & 12 \\ 4 & 12 & 1 & 12 & 6 & 2 & 3 & 4 \\ 12 & 4 & 12 & 1 & 2 & 6 & 4 & 3 \\ 6 & 2 & 6 & 2 & 1 & 3 & 2 & 6 \\ 2 & 6 & 2 & 6 & 3 & 1 & 6 & 2 \\ 12 & 4 & 3 & 4 & 2 & 6 & 1 & 12 \\ 4 & 12 & 4 & 3 & 6 & 2 & 12 & 1 \end{array}\right)\)

Isogeny graph