Properties

Base field \(\Q(\sqrt{-3}) \)
Label 2.0.3.1-5329.1-a
Conductor 5329.1
Rank \( 1 \)

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 5329.1-a over \(\Q(\sqrt{-3}) \)

Isogeny class 5329.1-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label Weierstrass Coefficients
5329.1-a1 \( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( 553 a + 535\) , \( 9628 a - 12840\bigr] \)
5329.1-a2 \( \bigl[a\) , \( a - 1\) , \( a\) , \( 75 a + 341\) , \( 3389 a - 2532\bigr] \)
5329.1-a3 \( \bigl[a\) , \( a - 1\) , \( a\) , \( -10 a + 26\) , \( 71 a - 95\bigr] \)
5329.1-a4 \( \bigl[a + 1\) , \( a\) , \( a + 1\) , \( 868 a + 135\) , \( 18504 a - 12861\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 6 & 3 & 2 \\ 6 & 1 & 2 & 3 \\ 3 & 2 & 1 & 6 \\ 2 & 3 & 6 & 1 \end{array}\right)\)

Isogeny graph