Properties

Base field \(\Q(\sqrt{-11}) \)
Label 2.0.11.1-225.3-b
Conductor 225.3
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 225.3-b over \(\Q(\sqrt{-11}) \)

Isogeny class 225.3-b contains 4 curves linked by isogenies of degrees dividing 15.

Curve label Weierstrass Coefficients
225.3-b1 \( \bigl[1\) , \( a - 1\) , \( a\) , \( 23 a + 93\) , \( 272 a - 400\bigr] \)
225.3-b2 \( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( 6 a + 3\) , \( 18 a - 23\bigr] \)
225.3-b3 \( \bigl[1\) , \( a - 1\) , \( a + 1\) , \( 8 a - 20\) , \( -18 a + 25\bigr] \)
225.3-b4 \( \bigl[a\) , \( 0\) , \( 0\) , \( -13 a - 27\) , \( 44 a + 50\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 15 & 5 \\ 3 & 1 & 5 & 15 \\ 15 & 5 & 1 & 3 \\ 5 & 15 & 3 & 1 \end{array}\right)\)

Isogeny graph