Properties

Base field \(\Q(\sqrt{57}) \)
Label 2.2.57.1-196.1-b
Conductor 196.1
Rank \( 1 \)

Related objects

Learn more

Base field \(\Q(\sqrt{57}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 14 \); class number \(1\).

Elliptic curves in class 196.1-b over \(\Q(\sqrt{57}) \)

Isogeny class 196.1-b contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
196.1-b1 \( \bigl[1\) , \( 1\) , \( 0\) , \( -362 a - 1185\) , \( -8952728 a - 29319443\bigr] \)
196.1-b2 \( \bigl[1\) , \( a - 1\) , \( a\) , \( -1226 a + 5243\) , \( -8599 a + 36757\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph