Properties

Base field \(\Q(\sqrt{19}) \)
Label 2.2.76.1-171.1-b
Conductor 171.1
Rank \( 0 \)

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Base field \(\Q(\sqrt{19}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 19 \); class number \(1\).

Elliptic curves in class 171.1-b over \(\Q(\sqrt{19}) \)

Isogeny class 171.1-b contains 2 curves linked by isogenies of degree 5.

Curve label Weierstrass Coefficients
171.1-b1 \( \bigl[0\) , \( 1\) , \( 1\) , \( -4390\) , \( -113432\bigr] \)
171.1-b2 \( \bigl[0\) , \( 1\) , \( 1\) , \( 20\) , \( -32\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph