Properties

Base field \(\Q(\sqrt{14}) \)
Label 2.2.56.1-200.1-g
Conductor 200.1
Rank not recorded

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Base field \(\Q(\sqrt{14}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 14 \); class number \(1\).

Elliptic curves in class 200.1-g over \(\Q(\sqrt{14}) \)

Isogeny class 200.1-g contains 4 curves linked by isogenies of degrees dividing 4.

Curve label Weierstrass Coefficients
200.1-g1 \( \bigl[a\) , \( 1\) , \( a\) , \( -390 a + 1459\) , \( 14698 a - 54995\bigr] \)
200.1-g2 \( \bigl[a\) , \( 1\) , \( a\) , \( 210 a - 786\) , \( 3012 a - 11270\bigr] \)
200.1-g3 \( \bigl[0\) , \( 0\) , \( 0\) , \( -2\) , \( 1\bigr] \)
200.1-g4 \( \bigl[a\) , \( 1\) , \( a\) , \( -3210 a - 12011\) , \( -196302 a - 734495\bigr] \)

Rank

Rank not yet determined.

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph