Properties

Base field \(\Q(\sqrt{-11}) \)
Label 2.0.11.1-27225.2-b
Conductor 27225.2
Rank \( 0 \)

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 27225.2-b over \(\Q(\sqrt{-11}) \)

Isogeny class 27225.2-b contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
27225.2-b1 \( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( -11 a + 28\) , \( -11 a + 30\bigr] \)
27225.2-b2 \( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( 44 a - 137\) , \( -220 a + 360\bigr] \)
27225.2-b3 \( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( 319 a - 962\) , \( 4895 a - 9540\bigr] \)
27225.2-b4 \( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( 649 a - 1952\) , \( -16071 a + 29400\bigr] \)

Rank

Rank: \( 0 \)

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