Properties

Base field \(\Q(\sqrt{3}) \)
Label 2.2.12.1-726.1-i
Conductor 726.1
Rank \( 0 \)

Related objects

Learn more

Base field \(\Q(\sqrt{3}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 3 \); class number \(1\).

Elliptic curves in class 726.1-i over \(\Q(\sqrt{3}) \)

Isogeny class 726.1-i contains 4 curves linked by isogenies of degrees dividing 10.

Curve label Weierstrass Coefficients
726.1-i1 \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 563080 a - 975335\) , \( 304441020 a - 527307459\bigr] \)
726.1-i2 \( \bigl[1\) , \( 0\) , \( 0\) , \( 115\) , \( 561\bigr] \)
726.1-i3 \( \bigl[1\) , \( 0\) , \( 0\) , \( -45\) , \( 81\bigr] \)
726.1-i4 \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 563640 a - 976305\) , \( 303809220 a - 526213149\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 5 & 10 & 2 \\ 5 & 1 & 2 & 10 \\ 10 & 2 & 1 & 5 \\ 2 & 10 & 5 & 1 \end{array}\right)\)

Isogeny graph