Properties

Base field \(\Q(\sqrt{-3}) \)
Label 2.0.3.1-12348.3-b
Conductor 12348.3
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 12348.3-b over \(\Q(\sqrt{-3}) \)

Isogeny class 12348.3-b contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
12348.3-b1 \( \bigl[a\) , \( -1\) , \( 1\) , \( -61 a + 97\) , \( -383 a - 385\bigr] \)
12348.3-b2 \( \bigl[a\) , \( -1\) , \( 1\) , \( 5789 a - 9263\) , \( -69683 a - 53557\bigr] \)
12348.3-b3 \( \bigl[a\) , \( -1\) , \( 1\) , \( -1561 a + 2497\) , \( -7943 a - 8281\bigr] \)
12348.3-b4 \( \bigl[a\) , \( -1\) , \( 1\) , \( -13711 a + 21937\) , \( 638437 a + 529235\bigr] \)
12348.3-b5 \( \bigl[a\) , \( -1\) , \( 1\) , \( -1261 a + 2017\) , \( -17183 a - 15841\bigr] \)
12348.3-b6 \( \bigl[a\) , \( -1\) , \( 1\) , \( -20161 a + 32257\) , \( -1128503 a - 978985\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph