Properties

Base field \(\Q(\sqrt{-3}) \)
Label 2.0.3.1-20736.1-e
Conductor 20736.1
Rank \( 0 \)

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 20736.1-e over \(\Q(\sqrt{-3}) \)

Isogeny class 20736.1-e contains 5 curves linked by isogenies of degrees dividing 9.

Curve label Weierstrass Coefficients
20736.1-e1 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -159 a - 327\) , \( 1657 a + 2032\bigr] \)
20736.1-e2 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( -486 a + 327\) , \( 1657 a - 3689\bigr] \)
20736.1-e3 \( \bigl[0\) , \( 0\) , \( 0\) , \( 153 a - 153\) , \( 852 a - 426\bigr] \)
20736.1-e4 \( \bigl[0\) , \( a + 1\) , \( 0\) , \( 74 a - 73\) , \( -343 a + 135\bigr] \)
20736.1-e5 \( \bigl[0\) , \( 0\) , \( 0\) , \( -63 a + 63\) , \( -156 a + 78\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph