Properties

Base field \(\Q(\sqrt{-3}) \)
Label 2.0.3.1-50625.1-f
Conductor 50625.1
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 50625.1-f over \(\Q(\sqrt{-3}) \)

Isogeny class 50625.1-f contains 2 curves linked by isogenies of degree 7.

Curve label Weierstrass Coefficients
50625.1-f1 \( \bigl[1\) , \( -1\) , \( a + 1\) , \( 52 a - 65\) , \( 183 a - 129\bigr] \)
50625.1-f2 \( \bigl[a + 1\) , \( 0\) , \( a\) , \( -13 a + 65\) , \( -184 a + 55\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph