Properties

Base field \(\Q(\sqrt{33}) \)
Label 2.2.33.1-576.4-i
Conductor 576.4
Rank \( 1 \)

Related objects

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Base field \(\Q(\sqrt{33}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 8 \); class number \(1\).

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph

Elliptic curves in class 576.4-i over \(\Q(\sqrt{33}) \)

Isogeny class 576.4-i contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
576.4-i1 \( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( -769 a - 1825\) , \( 18028 a + 42767\bigr] \)
576.4-i2 \( \bigl[a + 1\) , \( a + 1\) , \( a + 1\) , \( -55 a + 203\) , \( 1156 a - 3877\bigr] \)