Properties

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

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

Curve label Weierstrass Coefficients
27225.5-h1 \( \bigl[a\) , \( a - 1\) , \( a\) , \( 167 a + 534\) , \( 3488 a - 6207\bigr] \)
27225.5-h2 \( \bigl[a\) , \( a - 1\) , \( a\) , \( -163 a + 424\) , \( -956 a - 2445\bigr] \)
27225.5-h3 \( \bigl[a\) , \( a - 1\) , \( a\) , \( 2 a + 39\) , \( 56 a - 168\bigr] \)
27225.5-h4 \( \bigl[a\) , \( a - 1\) , \( a\) , \( 2 a - 16\) , \( a - 14\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph