Properties

Base field \(\Q(\sqrt{21}) \)
Label 2.2.21.1-2100.1-bl
Conductor 2100.1
Rank not recorded

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-bl over \(\Q(\sqrt{21}) \)

Isogeny class 2100.1-bl contains 12 curves linked by isogenies of degrees dividing 24.

Curve label Weierstrass Coefficients
2100.1-bl1 \( \bigl[a + 1\) , \( -a + 1\) , \( a\) , \( -1706044 a - 3300813\) , \( 1911947903 a + 3471227548\bigr] \)
2100.1-bl2 \( \bigl[a\) , \( 1\) , \( a + 1\) , \( 101762 a - 284936\) , \( -34547608 a + 96444555\bigr] \)
2100.1-bl3 \( \bigl[a + 1\) , \( -a + 1\) , \( a\) , \( 1581 a - 188\) , \( 7772728 a + 13984173\bigr] \)
2100.1-bl4 \( \bigl[a\) , \( 1\) , \( a + 1\) , \( -9613 a + 26914\) , \( 488537 a - 1363755\bigr] \)
2100.1-bl5 \( \bigl[a\) , \( 1\) , \( a + 1\) , \( 2887 a - 8086\) , \( 69037 a - 192755\bigr] \)
2100.1-bl6 \( \bigl[a\) , \( 1\) , \( a + 1\) , \( 7362 a - 20616\) , \( -392280 a + 1095051\bigr] \)
2100.1-bl7 \( \bigl[a + 1\) , \( -a + 1\) , \( a\) , \( -21789 a - 39218\) , \( 2597374 a + 4653447\bigr] \)
2100.1-bl8 \( \bigl[a\) , \( 1\) , \( a + 1\) , \( 2487 a - 6966\) , \( 103965 a - 290259\bigr] \)
2100.1-bl9 \( \bigl[a\) , \( 1\) , \( a + 1\) , \( 109762 a - 307336\) , \( -29977688 a + 83686795\bigr] \)
2100.1-bl10 \( \bigl[a\) , \( 1\) , \( a + 1\) , \( -1583 a + 1394\) , \( -7772729 a + 21756901\bigr] \)
2100.1-bl11 \( \bigl[a\) , \( 1\) , \( a + 1\) , \( 1756162 a - 4917256\) , \( -1921823000 a + 5365074571\bigr] \)
2100.1-bl12 \( \bigl[a\) , \( 1\) , \( a + 1\) , \( 1706042 a - 5006856\) , \( -1911947904 a + 5383175451\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

\(\left(\begin{array}{rrrrrrrrrrrr} 1 & 8 & 3 & 24 & 12 & 8 & 6 & 24 & 4 & 12 & 2 & 4 \\ 8 & 1 & 24 & 3 & 6 & 4 & 12 & 12 & 2 & 24 & 4 & 8 \\ 3 & 24 & 1 & 8 & 4 & 24 & 2 & 8 & 12 & 4 & 6 & 12 \\ 24 & 3 & 8 & 1 & 2 & 12 & 4 & 4 & 6 & 8 & 12 & 24 \\ 12 & 6 & 4 & 2 & 1 & 6 & 2 & 2 & 3 & 4 & 6 & 12 \\ 8 & 4 & 24 & 12 & 6 & 1 & 12 & 3 & 2 & 24 & 4 & 8 \\ 6 & 12 & 2 & 4 & 2 & 12 & 1 & 4 & 6 & 2 & 3 & 6 \\ 24 & 12 & 8 & 4 & 2 & 3 & 4 & 1 & 6 & 8 & 12 & 24 \\ 4 & 2 & 12 & 6 & 3 & 2 & 6 & 6 & 1 & 12 & 2 & 4 \\ 12 & 24 & 4 & 8 & 4 & 24 & 2 & 8 & 12 & 1 & 6 & 3 \\ 2 & 4 & 6 & 12 & 6 & 4 & 3 & 12 & 2 & 6 & 1 & 2 \\ 4 & 8 & 12 & 24 & 12 & 8 & 6 & 24 & 4 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph