Properties

Base field \(\Q(\sqrt{3}) \)
Label 2.2.12.1-512.1-h
Conductor 512.1
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 512.1-h over \(\Q(\sqrt{3}) \)

Isogeny class 512.1-h contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
512.1-h1 \( \bigl[0\) , \( a\) , \( 0\) , \( 220 a - 380\) , \( -2464 a + 4268\bigr] \)
512.1-h2 \( \bigl[0\) , \( a\) , \( 0\) , \( 15 a - 25\) , \( -38 a + 66\bigr] \)
512.1-h3 \( \bigl[0\) , \( a\) , \( 0\) , \( -6 a - 11\) , \( -15 a - 26\bigr] \)
512.1-h4 \( \bigl[0\) , \( a\) , \( 0\) , \( -40 a + 70\) , \( -172 a + 298\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph