Properties

Base field \(\Q(\sqrt{3}) \)
Label 2.2.12.1-726.1-l
Conductor 726.1
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 726.1-l over \(\Q(\sqrt{3}) \)

Isogeny class 726.1-l contains 4 curves linked by isogenies of degrees dividing 6.

Curve label Weierstrass Coefficients
726.1-l1 \( \bigl[1\) , \( a\) , \( 0\) , \( -32 a - 115\) , \( 444 a + 17\bigr] \)
726.1-l2 \( \bigl[1\) , \( a\) , \( 0\) , \( 2728 a - 3850\) , \( 87888 a - 149212\bigr] \)
726.1-l3 \( \bigl[1\) , \( a\) , \( 0\) , \( 38568 a - 70410\) , \( 5632848 a - 9738972\bigr] \)
726.1-l4 \( \bigl[1\) , \( a\) , \( 0\) , \( -312 a - 2235\) , \( 23220 a + 14265\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph