Properties

Base field \(\Q(\sqrt{-11}) \)
Label 2.0.11.1-27225.4-b
Conductor 27225.4
Rank \( 1 \)

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 27225.4-b over \(\Q(\sqrt{-11}) \)

Isogeny class 27225.4-b contains 2 curves linked by isogenies of degree 3.

Curve label Weierstrass Coefficients
27225.4-b1 \( \bigl[0\) , \( -1\) , \( a + 1\) , \( 33 a - 205\) , \( 486 a - 762\bigr] \)
27225.4-b2 \( \bigl[0\) , \( -1\) , \( a + 1\) , \( -187 a + 400\) , \( -702 a - 2995\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph