Elliptic curve isogeny class 200.1-g over number field \(\Q(\sqrt{14}) \)

• Base field: \(\Q(\sqrt{14}) \)
• Label: 2.2.56.1-200.1-g
• Conductor: 200.1
• Rank: \( 0 \)

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: \( 0 \)

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