Properties

Base field \(\Q(\sqrt{3}) \)
Label 2.2.12.1-288.1-a
Conductor 288.1
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 288.1-a over \(\Q(\sqrt{3}) \)

Isogeny class 288.1-a contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
288.1-a1 \( \bigl[0\) , \( -a\) , \( 0\) , \( 4063804 a - 7038714\) , \( -5839863922 a + 10114941022\bigr] \)
288.1-a2 \( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 381758 a - 661224\) , \( 168866036 a - 292484554\bigr] \)
288.1-a3 \( \bigl[a + 1\) , \( -1\) , \( 0\) , \( 23873 a - 41349\) , \( 2630312 a - 4555834\bigr] \)
288.1-a4 \( \bigl[0\) , \( -a\) , \( 0\) , \( 113682 a - 196902\) , \( 3469554 a - 6009444\bigr] \)
288.1-a5 \( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( 77 a - 140\) , \( 1663 a - 2881\bigr] \)
288.1-a6 \( \bigl[a + 1\) , \( -1\) , \( 0\) , \( -1569806 a + 2718984\) , \( 176681708 a - 306021695\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph