Properties

Base field \(\Q(\sqrt{3}) \)
Label 2.2.12.1-507.1-e
Conductor 507.1
Rank \( 1 \)

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 507.1-e over \(\Q(\sqrt{3}) \)

Isogeny class 507.1-e contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
507.1-e1 \( \bigl[a\) , \( 1\) , \( a\) , \( 95 a - 140\) , \( 602 a - 1176\bigr] \)
507.1-e2 \( \bigl[1\) , \( -a\) , \( 1\) , \( -27 a + 47\) , \( -230 a + 398\bigr] \)
507.1-e3 \( \bigl[a\) , \( 1\) , \( a\) , \( -5\) , \( 0\bigr] \)
507.1-e4 \( \bigl[a\) , \( 1\) , \( a\) , \( -20\) , \( -42\bigr] \)
507.1-e5 \( \bigl[a\) , \( 1\) , \( a\) , \( -70\) , \( 182\bigr] \)
507.1-e6 \( \bigl[a\) , \( 1\) , \( a\) , \( -95 a - 140\) , \( -602 a - 1176\bigr] \)

Rank

Rank: \( 1 \)

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