Properties

Base field \(\Q(\sqrt{55}) \)
Label 2.2.220.1-11.1-d
Conductor 11.1
Rank \( 0 \)

Related objects

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Base field \(\Q(\sqrt{55}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 55 \); class number \(2\).

Elliptic curves in class 11.1-d over \(\Q(\sqrt{55}) \)

Isogeny class 11.1-d contains 3 curves linked by isogenies of degrees dividing 25.

Curve label Weierstrass Coefficients
11.1-d1 \( \bigl[0\) , \( -1\) , \( a\) , \( -16704232 a - 123881900\) , \( 101208607111 a + 750583118924\bigr] \)
11.1-d2 \( \bigl[0\) , \( -1\) , \( a\) , \( 22072 a - 163690\) , \( -8811711 a + 65349384\bigr] \)
11.1-d3 \( \bigl[0\) , \( -1\) , \( a\) , \( 712 a - 5280\) , \( 66649 a - 494296\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph