Properties

Base field \(\Q(\sqrt{-67}) \)
Label 2.0.67.1-323.1-a
Conductor 323.1
Rank \( 1 \)

Related objects

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Base field \(\Q(\sqrt{-67}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x + 17 \); class number \(1\).

Elliptic curves in class 323.1-a over \(\Q(\sqrt{-67}) \)

Isogeny class 323.1-a contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
323.1-a1 \( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( -16 a + 79\) , \( 27 a + 217\bigr] \)
323.1-a2 \( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( -11 a + 84\) , \( -5 a + 394\bigr] \)
323.1-a3 \( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( -a - 1\) , \( 0\bigr] \)
323.1-a4 \( \bigl[1\) , \( -a - 1\) , \( a + 1\) , \( -261 a + 1354\) , \( 2647 a + 18968\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph