Properties

Base field \(\Q(\sqrt{-11}) \)
Label 2.0.11.1-27225.7-e
Conductor 27225.7
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 27225.7-e over \(\Q(\sqrt{-11}) \)

Isogeny class 27225.7-e contains 3 curves linked by isogenies of degrees dividing 25.

Curve label Weierstrass Coefficients
27225.7-e1 \( \bigl[0\) , \( -a + 1\) , \( 1\) , \( -602166 a + 1118307\) , \( 81612670 a + 506323495\bigr] \)
27225.7-e2 \( \bigl[0\) , \( -a + 1\) , \( 1\) , \( -796 a + 1477\) , \( 6640 a + 43765\bigr] \)
27225.7-e3 \( \bigl[0\) , \( -a + 1\) , \( 1\) , \( -26 a + 47\) , \( -70 a - 345\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 5 & 25 \\ 5 & 1 & 5 \\ 25 & 5 & 1 \end{array}\right)\)

Isogeny graph