Properties

Base field \(\Q(\sqrt{-3}) \)
Label 2.0.3.1-99372.6-h
Conductor 99372.6
Rank \( 1 \)

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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 99372.6-h over \(\Q(\sqrt{-3}) \)

Isogeny class 99372.6-h contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
99372.6-h1 \( \bigl[a\) , \( -a - 1\) , \( a\) , \( -60 a + 33\) , \( -215 a + 335\bigr] \)
99372.6-h2 \( \bigl[a\) , \( -a - 1\) , \( a\) , \( 5790 a - 3087\) , \( -43277 a + 61901\bigr] \)
99372.6-h3 \( \bigl[a\) , \( -a - 1\) , \( a\) , \( -1560 a + 833\) , \( -4371 a + 6923\bigr] \)
99372.6-h4 \( \bigl[a\) , \( -a - 1\) , \( a\) , \( -13710 a + 7313\) , \( 386535 a - 564775\bigr] \)
99372.6-h5 \( \bigl[a\) , \( -a - 1\) , \( a\) , \( -1260 a + 673\) , \( -9991 a + 15103\bigr] \)
99372.6-h6 \( \bigl[a\) , \( -a - 1\) , \( a\) , \( -20160 a + 10753\) , \( -671995 a + 995635\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph