Properties

Base field \(\Q(\sqrt{33}) \)
Label 2.2.33.1-588.1-k
Conductor 588.1
Rank \( 0 \)

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: \( 0 \)

Isogeny matrix

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

Isogeny graph

Elliptic curves in class 588.1-k over \(\Q(\sqrt{33}) \)

Isogeny class 588.1-k contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
588.1-k1 \( \bigl[1\) , \( a + 1\) , \( 1\) , \( 26 a - 83\) , \( -125 a + 423\bigr] \)
588.1-k2 \( \bigl[1\) , \( -a - 1\) , \( 1\) , \( 551 a - 1853\) , \( -93367 a + 314857\bigr] \)