Elliptic curve isogeny class 100.1-f over number field \(\Q(\sqrt{14}) \)

• Base field: \(\Q(\sqrt{14}) \)
• Label: 2.2.56.1-100.1-f
• Conductor: 100.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 100.1-f over \(\Q(\sqrt{14}) \)

Isogeny class 100.1-f contains 4 curves linked by isogenies of degrees dividing 6.

Curve label	Weierstrass Coefficients
100.1-f1	\( \bigl[a\) , \( -a + 1\) , \( 0\) , \( -1093 a - 4067\) , \( -57781 a - 216176\bigr] \)
100.1-f2	\( \bigl[a\) , \( a + 1\) , \( 0\) , \( -107 a + 423\) , \( -1257 a + 4724\bigr] \)
100.1-f3	\( \bigl[0\) , \( 1\) , \( 0\) , \( -1\) , \( 0\bigr] \)
100.1-f4	\( \bigl[0\) , \( 1\) , \( 0\) , \( -41\) , \( -116\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph