Properties

Base field \(\Q(\sqrt{53}) \)
Label 2.2.53.1-49.3-b
Conductor 49.3
Rank \( 1 \)

Related objects

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Base field \(\Q(\sqrt{53}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 13 \); class number \(1\).

Elliptic curves in class 49.3-b over \(\Q(\sqrt{53}) \)

Isogeny class 49.3-b contains 2 curves linked by isogenies of degree 7.

Curve label Weierstrass Coefficients
49.3-b1 \( \bigl[0\) , \( -1\) , \( a\) , \( 2 a - 8\) , \( 5 a - 25\bigr] \)
49.3-b2 \( \bigl[0\) , \( -1\) , \( a\) , \( 232 a - 978\) , \( -3994 a + 16508\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph