Properties

Base field \(\Q(\sqrt{13}) \)
Label 2.2.13.1-52.1-b
Conductor 52.1
Rank not recorded

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Base field \(\Q(\sqrt{13}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 3 \); class number \(1\).

Elliptic curves in class 52.1-b over \(\Q(\sqrt{13}) \)

Isogeny class 52.1-b contains 2 curves linked by isogenies of degree 7.

Curve label Weierstrass Coefficients
52.1-b1 \( \bigl[1\) , \( -1\) , \( 1\) , \( -213\) , \( -1257\bigr] \)
52.1-b2 \( \bigl[1\) , \( -1\) , \( 1\) , \( -3\) , \( 3\bigr] \)

Rank

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Isogeny matrix

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

Isogeny graph