Properties

Base field \(\Q(\sqrt{209}) \)
Label 2.2.209.1-4.1-c
Conductor 4.1
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 4.1-c over \(\Q(\sqrt{209}) \)

Isogeny class 4.1-c contains 4 curves linked by isogenies of degrees dividing 10.

Curve label Weierstrass Coefficients
4.1-c1 \( \bigl[1\) , \( -1\) , \( 1\) , \( 25 a - 196\) , \( -132 a + 1019\bigr] \)
4.1-c2 \( \bigl[1\) , \( -1\) , \( 1\) , \( 109626655 a - 847240411\) , \( 1679777810708 a - 12982021956321\bigr] \)
4.1-c3 \( \bigl[1\) , \( -1\) , \( 1\) , \( -25 a - 171\) , \( 132 a + 887\bigr] \)
4.1-c4 \( \bigl[1\) , \( -1\) , \( 1\) , \( -109626655 a - 737613756\) , \( -1679777810708 a - 11302244145613\bigr] \)

Rank

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Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 5 & 10 & 2 \\ 5 & 1 & 2 & 10 \\ 10 & 2 & 1 & 5 \\ 2 & 10 & 5 & 1 \end{array}\right)\)

Isogeny graph