Properties

Base field \(\Q(\sqrt{-3}) \)
Label 2.0.3.1-33124.5-c
Conductor 33124.5
Rank not recorded

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 33124.5-c over \(\Q(\sqrt{-3}) \)

Isogeny class 33124.5-c contains 5 curves linked by isogenies of degrees dividing 9.

Curve label Weierstrass Coefficients
33124.5-c1 \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -15663 a + 15663\) , \( -755809\bigr] \)
33124.5-c2 \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -193 a + 193\) , \( -1055\bigr] \)
33124.5-c3 \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -23 a + 1093\) , \( 16670 a - 8609\bigr] \)
33124.5-c4 \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( -1093 a + 23\) , \( -16670 a + 8061\bigr] \)
33124.5-c5 \( \bigl[a + 1\) , \( -a\) , \( 0\) , \( 7 a - 7\) , \( -7\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

\(\left(\begin{array}{rrrrr} 1 & 3 & 9 & 9 & 9 \\ 3 & 1 & 3 & 3 & 3 \\ 9 & 3 & 1 & 9 & 9 \\ 9 & 3 & 9 & 1 & 9 \\ 9 & 3 & 9 & 9 & 1 \end{array}\right)\)

Isogeny graph