Properties

Base field \(\Q(\sqrt{53}) \)
Label 2.2.53.1-49.2-a
Conductor 49.2
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 49.2-a over \(\Q(\sqrt{53}) \)

Isogeny class 49.2-a contains 2 curves linked by isogenies of degree 7.

Curve label Weierstrass Coefficients
49.2-a1 \( \bigl[0\) , \( -a - 1\) , \( a + 1\) , \( -7698 a - 29615\) , \( 842473 a + 2486905\bigr] \)
49.2-a2 \( \bigl[0\) , \( -a - 1\) , \( a + 1\) , \( 2 a - 5\) , \( 16 a + 57\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph