Properties

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

Isogeny class 27225.5-d contains 8 curves linked by isogenies of degrees dividing 12.

Curve label Weierstrass Coefficients
27225.5-d1 \( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( -14841 a + 10974\) , \( -481824 a + 1498478\bigr] \)
27225.5-d2 \( \bigl[1\) , \( 1\) , \( a + 1\) , \( 225 a - 437\) , \( -2363 a + 2243\bigr] \)
27225.5-d3 \( \bigl[1\) , \( 1\) , \( a + 1\) , \( 5 a - 5992\) , \( -350 a - 182029\bigr] \)
27225.5-d4 \( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( -926 a + 689\) , \( -7141 a + 22641\bigr] \)
27225.5-d5 \( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( -46 a - 26\) , \( 75 a + 740\bigr] \)
27225.5-d6 \( \bigl[a\) , \( -a - 1\) , \( a + 1\) , \( -1091 a + 1844\) , \( -20902 a + 168\bigr] \)
27225.5-d7 \( \bigl[1\) , \( 1\) , \( a + 1\) , \( 170 a - 547\) , \( -2726 a - 562\bigr] \)
27225.5-d8 \( \bigl[1\) , \( 1\) , \( a + 1\) , \( -545 a + 3138\) , \( -27234 a + 3585\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrrrr} 1 & 12 & 12 & 2 & 4 & 4 & 6 & 3 \\ 12 & 1 & 4 & 6 & 3 & 12 & 2 & 4 \\ 12 & 4 & 1 & 6 & 12 & 3 & 2 & 4 \\ 2 & 6 & 6 & 1 & 2 & 2 & 3 & 6 \\ 4 & 3 & 12 & 2 & 1 & 4 & 6 & 12 \\ 4 & 12 & 3 & 2 & 4 & 1 & 6 & 12 \\ 6 & 2 & 2 & 3 & 6 & 6 & 1 & 2 \\ 3 & 4 & 4 & 6 & 12 & 12 & 2 & 1 \end{array}\right)\)

Isogeny graph