Properties

Base field \(\Q(\sqrt{-3}) \)
Label 2.0.3.1-15876.1-a
Conductor 15876.1
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 15876.1-a over \(\Q(\sqrt{-3}) \)

Isogeny class 15876.1-a contains 2 curves linked by isogenies of degree 7.

Curve label Weierstrass Coefficients
15876.1-a1 \( \bigl[a\) , \( -a + 1\) , \( a\) , \( -5 a + 5\) , \( 2 a + 2\bigr] \)
15876.1-a2 \( \bigl[a\) , \( -a + 1\) , \( a\) , \( -5 a - 625\) , \( 128 a - 6172\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph