Properties

Base field \(\Q(\sqrt{-3}) \)
Label 2.0.3.1-112896.2-v
Conductor 112896.2
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 112896.2-v over \(\Q(\sqrt{-3}) \)

Isogeny class 112896.2-v contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
112896.2-v1 \( \bigl[0\) , \( 0\) , \( 0\) , \( -3 a + 3\) , \( 12 a - 6\bigr] \)
112896.2-v2 \( \bigl[0\) , \( 0\) , \( 0\) , \( 177 a - 177\) , \( -828 a + 414\bigr] \)
112896.2-v3 \( \bigl[0\) , \( 0\) , \( 0\) , \( 57 a - 57\) , \( 180 a - 90\bigr] \)
112896.2-v4 \( \bigl[0\) , \( 0\) , \( 0\) , \( 897 a - 897\) , \( 11940 a - 5970\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph