Properties

Base field \(\Q(\sqrt{205}) \)
Label 2.2.205.1-27.2-a
Conductor 27.2
Rank \( 1 \)

Related objects

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Base field \(\Q(\sqrt{205}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 51 \); class number \(2\).

Elliptic curves in class 27.2-a over \(\Q(\sqrt{205}) \)

Isogeny class 27.2-a contains 4 curves linked by isogenies of degrees dividing 15.

Curve label Weierstrass Coefficients
27.2-a1 \( \bigl[0\) , \( a - 1\) , \( 1\) , \( 31 a - 340\) , \( -1400 a + 10962\bigr] \)
27.2-a2 \( \bigl[0\) , \( a - 1\) , \( 1\) , \( -39 a - 240\) , \( 430 a + 2846\bigr] \)
27.2-a3 \( \bigl[0\) , \( a - 1\) , \( 1\) , \( 391 a - 2980\) , \( 10278 a - 78708\bigr] \)
27.2-a4 \( \bigl[0\) , \( 0\) , \( 1\) , \( 348 a - 2664\) , \( 13874 a - 106258\bigr] \)

Rank

Rank: \( 1 \)

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