Properties

Base field \(\Q(\sqrt{3}) \)
Label 2.2.12.1-4608.1-x
Conductor 4608.1
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 4608.1-x over \(\Q(\sqrt{3}) \)

Isogeny class 4608.1-x contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
4608.1-x1 \( \bigl[0\) , \( -a\) , \( 0\) , \( 38 a - 75\) , \( 503 a - 898\bigr] \)
4608.1-x2 \( \bigl[0\) , \( -a\) , \( 0\) , \( 177172 a - 306870\) , \( 53526260 a - 92710202\bigr] \)
4608.1-x3 \( \bigl[0\) , \( -a\) , \( 0\) , \( 11077 a - 19185\) , \( 840548 a - 1455872\bigr] \)
4608.1-x4 \( \bigl[0\) , \( -a\) , \( 0\) , \( 14272 a - 24720\) , \( 322076 a - 557852\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph