Properties

Base field \(\Q(\sqrt{497}) \)
Label 2.2.497.1-4.1-b
Conductor 4.1
Rank \( 1 \)

Related objects

Learn more

Base field \(\Q(\sqrt{497}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 124 \); class number \(1\).

Elliptic curves in class 4.1-b over \(\Q(\sqrt{497}) \)

Isogeny class 4.1-b contains 2 curves linked by isogenies of degree 3.

Curve label Weierstrass Coefficients
4.1-b1 \( \bigl[1\) , \( 1\) , \( a + 1\) , \( -13672 a - 145557\) , \( 611456 a + 6509995\bigr] \)
4.1-b2 \( \bigl[1\) , \( 1\) , \( a + 1\) , \( -842727 a - 8972297\) , \( 1405587529 a + 14964936759\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph