Properties

Base field \(\Q(\sqrt{53}) \)
Label 2.2.53.1-212.1-c
Conductor 212.1
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 212.1-c over \(\Q(\sqrt{53}) \)

Isogeny class 212.1-c contains 2 curves linked by isogenies of degree 3.

Curve label Weierstrass Coefficients
212.1-c1 \( \bigl[1\) , \( 0\) , \( 0\) , \( -24603\) , \( -1487407\bigr] \)
212.1-c2 \( \bigl[1\) , \( 0\) , \( 0\) , \( -283\) , \( -2351\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph