Properties

Base field \(\Q(\sqrt{21}) \)
Label 2.2.21.1-45.2-b
Conductor 45.2
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 45.2-b over \(\Q(\sqrt{21}) \)

Isogeny class 45.2-b contains 6 curves linked by isogenies of degrees dividing 8.

Curve label Weierstrass Coefficients
45.2-b1 \( \bigl[a + 1\) , \( a + 1\) , \( 1\) , \( 3 a + 6\) , \( 4 a + 7\bigr] \)
45.2-b2 \( \bigl[a + 1\) , \( a + 1\) , \( 1\) , \( 273 a - 279\) , \( -1724 a + 5275\bigr] \)
45.2-b3 \( \bigl[a + 1\) , \( a + 1\) , \( 1\) , \( -12 a - 69\) , \( -110 a - 59\bigr] \)
45.2-b4 \( \bigl[a + 1\) , \( a + 1\) , \( 1\) , \( -12 a - 24\) , \( 16 a + 31\bigr] \)
45.2-b5 \( \bigl[a + 1\) , \( a + 1\) , \( 1\) , \( -297 a - 579\) , \( -5300 a - 9353\bigr] \)
45.2-b6 \( \bigl[a + 1\) , \( a + 1\) , \( 1\) , \( -252 a - 459\) , \( 2770 a + 4957\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph