Properties

Base field \(\Q(\sqrt{21}) \)
Label 2.2.21.1-2100.1-n
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-n over \(\Q(\sqrt{21}) \)

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

Curve label Weierstrass Coefficients
2100.1-n1 \( \bigl[1\) , \( 0\) , \( 1\) , \( 1149680 a - 3560313\) , \( 1101560992 a - 3154926684\bigr] \)
2100.1-n2 \( \bigl[1\) , \( 0\) , \( 1\) , \( -20353\) , \( -1443724\bigr] \)
2100.1-n3 \( \bigl[1\) , \( 0\) , \( 1\) , \( 15180 a - 42188\) , \( 1465392 a - 4414684\bigr] \)
2100.1-n4 \( \bigl[1\) , \( 0\) , \( 1\) , \( 1922\) , \( 20756\bigr] \)
2100.1-n5 \( \bigl[1\) , \( 0\) , \( 1\) , \( -578\) , \( 2756\bigr] \)
2100.1-n6 \( \bigl[1\) , \( 0\) , \( 1\) , \( -1473\) , \( -16652\bigr] \)
2100.1-n7 \( \bigl[1\) , \( 0\) , \( 1\) , \( -4358\) , \( -109132\bigr] \)
2100.1-n8 \( \bigl[1\) , \( 0\) , \( 1\) , \( -498\) , \( 4228\bigr] \)
2100.1-n9 \( \bigl[1\) , \( 0\) , \( 1\) , \( -21953\) , \( -1253644\bigr] \)
2100.1-n10 \( \bigl[1\) , \( 0\) , \( 1\) , \( -15180 a - 27008\) , \( -1465392 a - 2949292\bigr] \)
2100.1-n11 \( \bigl[1\) , \( 0\) , \( 1\) , \( -351233\) , \( -80149132\bigr] \)
2100.1-n12 \( \bigl[1\) , \( 0\) , \( 1\) , \( -1149680 a - 2410633\) , \( -1101560992 a - 2053365692\bigr] \)

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