Properties

Base field \(\Q(\sqrt{-11}) \)
Label 2.0.11.1-27225.4-a
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-a over \(\Q(\sqrt{-11}) \)

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

Curve label Weierstrass Coefficients
27225.4-a1 \( \bigl[a + 1\) , \( 1\) , \( a\) , \( 3 a - 5\) , \( 30 a - 21\bigr] \)
27225.4-a2 \( \bigl[a + 1\) , \( 1\) , \( a\) , \( -87 a - 70\) , \( 496 a + 10\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph