Properties

Base field \(\Q(\sqrt{209}) \)
Label 2.2.209.1-10.4-c
Conductor 10.4
Rank not recorded

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Base field \(\Q(\sqrt{209}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 52 \); class number \(1\).

Elliptic curves in class 10.4-c over \(\Q(\sqrt{209}) \)

Isogeny class 10.4-c contains 2 curves linked by isogenies of degree 2.

Curve label Weierstrass Coefficients
10.4-c1 \( \bigl[1\) , \( 1\) , \( 1\) , \( -512138585 a - 3445881525\) , \( -13200346700953 a - 88817425893977\bigr] \)
10.4-c2 \( \bigl[1\) , \( 1\) , \( 1\) , \( 0\) , \( -3 a + 23\bigr] \)

Rank

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Isogeny matrix

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph