Properties

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

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

Curve label Weierstrass Coefficients
27225.5-i1 \( \bigl[a\) , \( 1\) , \( a + 1\) , \( -25 a + 23\) , \( -49 a - 38\bigr] \)
27225.5-i2 \( \bigl[a\) , \( 1\) , \( a + 1\) , \( 140 a - 87\) , \( -390 a - 544\bigr] \)
27225.5-i3 \( \bigl[a\) , \( 1\) , \( a + 1\) , \( 855 a - 747\) , \( 11391 a + 2822\bigr] \)
27225.5-i4 \( \bigl[a\) , \( 1\) , \( a + 1\) , \( 2065 a - 1187\) , \( -34875 a - 33874\bigr] \)

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