Properties

Base field \(\Q(\sqrt{21}) \)
Label 2.2.21.1-2268.1-v
Conductor 2268.1
Rank \( 1 \)

Related objects

Learn more

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

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

Elliptic curves in class 2268.1-v over \(\Q(\sqrt{21}) \)

Isogeny class 2268.1-v contains 3 curves linked by isogenies of degrees dividing 9.

Curve label Weierstrass Coefficients
2268.1-v1 \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 5310 a - 14868\) , \( 326160 a - 910530\bigr] \)
2268.1-v2 \( \bigl[a\) , \( -a + 1\) , \( 0\) , \( 60 a - 168\) , \( 576 a - 1608\bigr] \)
2268.1-v3 \( \bigl[1\) , \( -1\) , \( 1\) , \( 10\) , \( 5\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph