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

• Base field: \(\Q(\sqrt{14}) \)
• Label: 2.2.56.1-200.1-f
• 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-f over \(\Q(\sqrt{14}) \)

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

Curve label	Weierstrass Coefficients
200.1-f1	\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( 4 a + 28\) , \( 12 a + 54\bigr] \)
200.1-f2	\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -36 a - 122\) , \( 164 a + 622\bigr] \)
200.1-f3	\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -206 a - 762\) , \( -2884 a - 10794\bigr] \)
200.1-f4	\( \bigl[a\) , \( -a - 1\) , \( 0\) , \( -506 a - 1882\) , \( 12140 a + 45430\bigr] \)

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