Properties

Base field \(\Q(\sqrt{53}) \)
Label 2.2.53.1-1183.6-g
Conductor 1183.6
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 1183.6-g over \(\Q(\sqrt{53}) \)

Isogeny class 1183.6-g contains 2 curves linked by isogenies of degree 7.

Curve label Weierstrass Coefficients
1183.6-g1 \( \bigl[0\) , \( a\) , \( a\) , \( 10 a - 39\) , \( 828 a - 3432\bigr] \)
1183.6-g2 \( \bigl[0\) , \( a\) , \( a\) , \( 112430 a - 466869\) , \( 39130751 a - 162025747\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph