Properties

Base field \(\Q(\sqrt{-11}) \)
Label 2.0.11.1-27225.9-g
Conductor 27225.9
Rank bounds 0...1

Related objects

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

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

Elliptic curves in class 27225.9-g over \(\Q(\sqrt{-11}) \)

Isogeny class 27225.9-g contains 2 curves linked by isogenies of degree 11.

Curve label Weierstrass Coefficients
27225.9-g1 \( \bigl[1\) , \( a + 1\) , \( 0\) , \( 2643 a - 3633\) , \( 81559 a - 36889\bigr] \)
27225.9-g2 \( \bigl[1\) , \( a + 1\) , \( 0\) , \( 3 a - 3\) , \( -5 a - 1\bigr] \)

Rank

Rank \(r\) satisfies \(0 \le r \le 1\)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 11 \\ 11 & 1 \end{array}\right)\)

Isogeny graph