Properties

Base field \(\Q(\sqrt{-3}) \)
Label 2.0.3.1-31684.1-a
Conductor 31684.1
Rank not recorded

Related objects

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

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

Elliptic curves in class 31684.1-a over \(\Q(\sqrt{-3}) \)

Isogeny class 31684.1-a contains 2 curves linked by isogenies of degree 3.

Curve label Weierstrass Coefficients
31684.1-a1 \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -554 a + 554\) , \( -5068\bigr] \)
31684.1-a2 \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 6 a - 6\) , \( -28\bigr] \)

Rank

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Isogeny matrix

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph