Properties

Base field \(\Q(\sqrt{-3}) \)
Label 2.0.3.1-3136.2-a
Conductor 3136.2
Rank \( 0 \)

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 3136.2-a over \(\Q(\sqrt{-3}) \)

Isogeny class 3136.2-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
3136.2-a1 \( \bigl[0\) , \( 0\) , \( 0\) , \( a - 1\) , \( 2\bigr] \)
3136.2-a2 \( \bigl[0\) , \( 0\) , \( 0\) , \( -59 a + 59\) , \( -138\bigr] \)
3136.2-a3 \( \bigl[0\) , \( 0\) , \( 0\) , \( -19 a + 19\) , \( 30\bigr] \)
3136.2-a4 \( \bigl[0\) , \( 0\) , \( 0\) , \( -299 a + 299\) , \( 1990\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph