Properties

Base field \(\Q(\sqrt{53}) \)
Label 2.2.53.1-49.1-c
Conductor 49.1
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 49.1-c over \(\Q(\sqrt{53}) \)

Isogeny class 49.1-c contains only one elliptic curve.

Curve label Weierstrass Coefficients
49.1-c1 \( \bigl[1\) , \( a + 1\) , \( a\) , \( a + 5\) , \( 4 a + 10\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{r} 1 \end{array}\right)\)

Isogeny graph