Properties

Base field \(\Q(\sqrt{-3}) \)
Label 2.0.3.1-124.2-a
Conductor 124.2
Rank \( 0 \)

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

Isogeny class 124.2-a contains 3 curves linked by isogenies of degrees dividing 25.

Curve label Weierstrass Coefficients
124.2-a1 \( \bigl[a\) , \( a - 1\) , \( a\) , \( -1301 a + 751\) , \( 10550 a - 16530\bigr] \)
124.2-a2 \( \bigl[a\) , \( a - 1\) , \( a\) , \( -a + 1\) , \( 0\bigr] \)
124.2-a3 \( \bigl[a\) , \( a - 1\) , \( a\) , \( 14 a - 9\) , \( -3 a + 9\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 25 & 5 \\ 25 & 1 & 5 \\ 5 & 5 & 1 \end{array}\right)\)

Isogeny graph