Properties

Base field \(\Q(\sqrt{-3}) \)
Label 2.0.3.1-12337.1-a
Conductor 12337.1
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 12337.1-a over \(\Q(\sqrt{-3}) \)

Isogeny class 12337.1-a contains 4 curves linked by isogenies of degrees dividing 6.

Curve label Weierstrass Coefficients
12337.1-a1 \( \bigl[a\) , \( -a\) , \( a\) , \( 141 a + 45\) , \( -389 a + 987\bigr] \)
12337.1-a2 \( \bigl[a\) , \( -a\) , \( a\) , \( -79 a + 35\) , \( -179 a + 213\bigr] \)
12337.1-a3 \( \bigl[a\) , \( -a\) , \( a\) , \( -4 a\) , \( -a + 6\bigr] \)
12337.1-a4 \( \bigl[a\) , \( -a\) , \( a\) , \( 181 a - 30\) , \( -1160 a + 1313\bigr] \)

Rank

Rank not yet determined.

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