Properties

Base field \(\Q(\sqrt{-11}) \)
Label 2.0.11.1-27225.5-g
Conductor 27225.5
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 27225.5-g over \(\Q(\sqrt{-11}) \)

Isogeny class 27225.5-g contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
27225.5-g1 \( \bigl[a + 1\) , \( -a + 1\) , \( a\) , \( 23 a - 1\) , \( 48 a - 86\bigr] \)
27225.5-g2 \( \bigl[a + 1\) , \( -a + 1\) , \( a\) , \( -142 a + 54\) , \( 389 a - 933\bigr] \)
27225.5-g3 \( \bigl[a + 1\) , \( -a + 1\) , \( a\) , \( -857 a + 109\) , \( -11392 a + 14214\bigr] \)
27225.5-g4 \( \bigl[a + 1\) , \( -a + 1\) , \( a\) , \( -2067 a + 879\) , \( 34874 a - 68748\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph