Properties

Base field \(\Q(\sqrt{-3}) \)
Label 2.0.3.1-61347.2-b
Conductor 61347.2
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 61347.2-b over \(\Q(\sqrt{-3}) \)

Isogeny class 61347.2-b contains 8 curves linked by isogenies of degrees dividing 16.

Curve label Weierstrass Coefficients
61347.2-b1 \( \bigl[a\) , \( 0\) , \( 0\) , \( -19876 a + 8030\) , \( -825374 a + 926773\bigr] \)
61347.2-b2 \( \bigl[a\) , \( 0\) , \( 0\) , \( -11846 a - 8030\) , \( 825374 a + 101399\bigr] \)
61347.2-b3 \( \bigl[a\) , \( 0\) , \( 0\) , \( 24 a\) , \( 63\bigr] \)
61347.2-b4 \( \bigl[a\) , \( 0\) , \( 0\) , \( -1341 a\) , \( 18228\bigr] \)
61347.2-b5 \( \bigl[a\) , \( 0\) , \( 0\) , \( 474 a\) , \( 2619\bigr] \)
61347.2-b6 \( \bigl[a\) , \( 0\) , \( 0\) , \( 3009 a\) , \( -61770\bigr] \)
61347.2-b7 \( \bigl[a\) , \( 0\) , \( 0\) , \( 429 a\) , \( 3384\bigr] \)
61347.2-b8 \( \bigl[a\) , \( 0\) , \( 0\) , \( 6864 a\) , \( 218313\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 4 & 16 & 2 & 4 & 8 & 8 & 16 \\ 4 & 1 & 16 & 2 & 4 & 8 & 8 & 16 \\ 16 & 16 & 1 & 8 & 4 & 8 & 2 & 4 \\ 2 & 2 & 8 & 1 & 2 & 4 & 4 & 8 \\ 4 & 4 & 4 & 2 & 1 & 2 & 2 & 4 \\ 8 & 8 & 8 & 4 & 2 & 1 & 4 & 8 \\ 8 & 8 & 2 & 4 & 2 & 4 & 1 & 2 \\ 16 & 16 & 4 & 8 & 4 & 8 & 2 & 1 \end{array}\right)\)

Isogeny graph