Properties

Base field \(\Q(\sqrt{21}) \)
Label 2.2.21.1-507.1-b
Conductor 507.1
Rank \( 2 \)

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 507.1-b over \(\Q(\sqrt{21}) \)

Isogeny class 507.1-b contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
507.1-b1 \( \bigl[a\) , \( a + 1\) , \( 0\) , \( 11\) , \( -5 a + 21\bigr] \)
507.1-b2 \( \bigl[a\) , \( a + 1\) , \( 0\) , \( 25 a - 59\) , \( -75 a + 216\bigr] \)
507.1-b3 \( \bigl[a\) , \( a + 1\) , \( 0\) , \( 100 a - 269\) , \( 723 a - 2013\bigr] \)
507.1-b4 \( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( -347 a - 623\) , \( 4730 a + 8476\bigr] \)

Rank

Rank: \( 2 \)

Isogeny matrix

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

Isogeny graph