Properties

Base field \(\Q(\sqrt{11}) \)
Label 2.2.44.1-198.1-d
Conductor 198.1
Rank \( 1 \)

Related objects

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Base field \(\Q(\sqrt{11}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 11 \); class number \(1\).

Elliptic curves in class 198.1-d over \(\Q(\sqrt{11}) \)

Isogeny class 198.1-d contains 4 curves linked by isogenies of degrees dividing 10.

Curve label Weierstrass Coefficients
198.1-d1 \( \bigl[1\) , \( 0\) , \( 0\) , \( -10055\) , \( -390309\bigr] \)
198.1-d2 \( \bigl[1\) , \( 0\) , \( 0\) , \( 115\) , \( 561\bigr] \)
198.1-d3 \( \bigl[1\) , \( 0\) , \( 0\) , \( -45\) , \( 81\bigr] \)
198.1-d4 \( \bigl[1\) , \( 0\) , \( 0\) , \( -10065\) , \( -389499\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 5 & 10 & 2 \\ 5 & 1 & 2 & 10 \\ 10 & 2 & 1 & 5 \\ 2 & 10 & 5 & 1 \end{array}\right)\)

Isogeny graph