Properties

Base field \(\Q(\sqrt{3}) \)
Label 2.2.12.1-1800.1-i
Conductor 1800.1
Rank \( 1 \)

Related objects

Learn more

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

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

Elliptic curves in class 1800.1-i over \(\Q(\sqrt{3}) \)

Isogeny class 1800.1-i contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
1800.1-i1 \( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -4 a - 5\) , \( 31 a + 53\bigr] \)
1800.1-i2 \( \bigl[a + 1\) , \( a - 1\) , \( a + 1\) , \( -124 a - 215\) , \( 871 a + 1511\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph