Properties

Base field \(\Q(\sqrt{-3}) \)
Label 2.0.3.1-71424.1-b
Conductor 71424.1
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 71424.1-b over \(\Q(\sqrt{-3}) \)

Isogeny class 71424.1-b contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
71424.1-b1 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 4 a + 4\) , \( 12 a\bigr] \)
71424.1-b2 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -a - 1\) , \( 0\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph