Properties

Base field \(\Q(\sqrt{-3}) \)
Label 2.0.3.1-50700.2-c
Conductor 50700.2
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 50700.2-c over \(\Q(\sqrt{-3}) \)

Isogeny class 50700.2-c contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
50700.2-c1 \( \bigl[a + 1\) , \( a\) , \( 0\) , \( -114 a + 114\) , \( -12978\bigr] \)
50700.2-c2 \( \bigl[a + 1\) , \( a\) , \( 0\) , \( 16 a - 16\) , \( 0\bigr] \)
50700.2-c3 \( \bigl[a + 1\) , \( a\) , \( 0\) , \( -64 a + 64\) , \( 112\bigr] \)
50700.2-c4 \( \bigl[a + 1\) , \( a\) , \( 0\) , \( -564 a + 564\) , \( -4788\bigr] \)
50700.2-c5 \( \bigl[a + 1\) , \( a\) , \( 0\) , \( -844 a + 844\) , \( 9940\bigr] \)
50700.2-c6 \( \bigl[a + 1\) , \( a\) , \( 0\) , \( -9014 a + 9014\) , \( -324198\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph