Properties

Base field \(\Q(\sqrt{-3}) \)
Label 2.0.3.1-2500.1-a
Conductor 2500.1
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 2500.1-a over \(\Q(\sqrt{-3}) \)

Isogeny class 2500.1-a contains 4 curves linked by isogenies of degrees dividing 15.

Curve label Weierstrass Coefficients
2500.1-a1 \( \bigl[1\) , \( 1\) , \( 1\) , \( -3138\) , \( -68969\bigr] \)
2500.1-a2 \( \bigl[1\) , \( 1\) , \( 1\) , \( -3\) , \( 1\bigr] \)
2500.1-a3 \( \bigl[a + 1\) , \( a\) , \( 0\) , \( -12 a + 12\) , \( -206\bigr] \)
2500.1-a4 \( \bigl[1\) , \( 1\) , \( 1\) , \( 22\) , \( -9\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 15 & 3 & 5 \\ 15 & 1 & 5 & 3 \\ 3 & 5 & 1 & 15 \\ 5 & 3 & 15 & 1 \end{array}\right)\)

Isogeny graph