Properties

Base field \(\Q(\sqrt{-3}) \)
Label 2.0.3.1-50700.3-b
Conductor 50700.3
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 50700.3-b over \(\Q(\sqrt{-3}) \)

Isogeny class 50700.3-b contains 8 curves linked by isogenies of degrees dividing 12.

Curve label Weierstrass Coefficients
50700.3-b1 \( \bigl[a\) , \( -a\) , \( 1\) , \( -203 a + 108\) , \( 2295 a - 3379\bigr] \)
50700.3-b2 \( \bigl[a\) , \( -a\) , \( 1\) , \( 22 a - 12\) , \( -81 a + 119\bigr] \)
50700.3-b3 \( \bigl[a\) , \( -a\) , \( 1\) , \( -6803 a + 3628\) , \( 19575 a - 28819\bigr] \)
50700.3-b4 \( \bigl[a\) , \( -a\) , \( 1\) , \( -1028 a + 548\) , \( 6975 a - 10269\bigr] \)
50700.3-b5 \( \bigl[a\) , \( -a\) , \( 1\) , \( -278 a + 148\) , \( -945 a + 1391\bigr] \)
50700.3-b6 \( \bigl[a\) , \( -a\) , \( 1\) , \( -5003 a + 2668\) , \( 85239 a - 125491\bigr] \)
50700.3-b7 \( \bigl[a\) , \( -a\) , \( 1\) , \( -4328 a + 2308\) , \( -67041 a + 98699\bigr] \)
50700.3-b8 \( \bigl[a\) , \( -a\) , \( 1\) , \( -80003 a + 42668\) , \( 5413239 a - 7969491\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 3 & 4 & 12 & 6 & 2 & 12 & 4 \\ 3 & 1 & 12 & 4 & 2 & 6 & 4 & 12 \\ 4 & 12 & 1 & 12 & 6 & 2 & 3 & 4 \\ 12 & 4 & 12 & 1 & 2 & 6 & 4 & 3 \\ 6 & 2 & 6 & 2 & 1 & 3 & 2 & 6 \\ 2 & 6 & 2 & 6 & 3 & 1 & 6 & 2 \\ 12 & 4 & 3 & 4 & 2 & 6 & 1 & 12 \\ 4 & 12 & 4 & 3 & 6 & 2 & 12 & 1 \end{array}\right)\)

Isogeny graph