Properties

Base field \(\Q(\sqrt{-11}) \)
Label 2.0.11.1-27225.6-b
Conductor 27225.6
Rank \( 1 \)

Related objects

Learn more

Base field \(\Q(\sqrt{-11}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x + 3 \); class number \(1\).

Elliptic curves in class 27225.6-b over \(\Q(\sqrt{-11}) \)

Isogeny class 27225.6-b contains 2 curves linked by isogenies of degree 3.

Curve label Weierstrass Coefficients
27225.6-b1 \( \bigl[0\) , \( -1\) , \( a\) , \( -33 a - 172\) , \( -487 a - 275\bigr] \)
27225.6-b2 \( \bigl[0\) , \( -1\) , \( a\) , \( 187 a + 213\) , \( 701 a - 3696\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph