Properties

Base field \(\Q(\sqrt{21}) \)
Label 2.2.21.1-2100.1-bk
Conductor 2100.1
Rank \( 0 \)

Related objects

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Base field \(\Q(\sqrt{21}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 5 \); class number \(1\).

Elliptic curves in class 2100.1-bk over \(\Q(\sqrt{21}) \)

Isogeny class 2100.1-bk contains 8 curves linked by isogenies of degrees dividing 12.

Curve label Weierstrass Coefficients
2100.1-bk1 \( \bigl[a\) , \( 1\) , \( a\) , \( 405 a - 1135\) , \( 157869 a - 440722\bigr] \)
2100.1-bk2 \( \bigl[a\) , \( 1\) , \( a\) , \( -3645 a + 10205\) , \( -4251285 a + 11868200\bigr] \)
2100.1-bk3 \( \bigl[a\) , \( 1\) , \( a\) , \( 205 a - 575\) , \( -731 a + 2038\bigr] \)
2100.1-bk4 \( \bigl[a\) , \( 1\) , \( a\) , \( 32255 a - 90315\) , \( 3030599 a - 8460692\bigr] \)
2100.1-bk5 \( \bigl[a\) , \( 1\) , \( a\) , \( 13505 a - 37815\) , \( -1254151 a + 3501058\bigr] \)
2100.1-bk6 \( \bigl[a\) , \( 1\) , \( a\) , \( 1805 a - 5055\) , \( 63845 a - 178250\bigr] \)
2100.1-bk7 \( \bigl[a\) , \( 1\) , \( a\) , \( 13405 a - 37535\) , \( -1274315 a + 3557350\bigr] \)
2100.1-bk8 \( \bigl[a\) , \( 1\) , \( a\) , \( 28805 a - 80655\) , \( 4056605 a - 11324930\bigr] \)

Rank

Rank: \( 0 \)

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