Properties

Base field \(\Q(\sqrt{21}) \)
Label 2.2.21.1-1452.1-e
Conductor 1452.1
Rank \( 1 \)

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 1452.1-e over \(\Q(\sqrt{21}) \)

Isogeny class 1452.1-e contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
1452.1-e1 \( \bigl[a\) , \( a + 1\) , \( 1\) , \( 62 a - 164\) , \( -1818 a + 5081\bigr] \)
1452.1-e2 \( \bigl[a\) , \( a + 1\) , \( 1\) , \( 12 a - 24\) , \( 2 a + 1\bigr] \)
1452.1-e3 \( \bigl[a\) , \( a + 1\) , \( 1\) , \( 112 a - 304\) , \( -950 a + 2657\bigr] \)
1452.1-e4 \( \bigl[a\) , \( a + 1\) , \( 1\) , \( 1762 a - 4924\) , \( -61010 a + 170297\bigr] \)

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