Elliptic curve isogeny class 81.1-a over number field \(\Q(\sqrt{14}) \)

• Base field: \(\Q(\sqrt{14}) \)
• Label: 2.2.56.1-81.1-a
• Conductor: 81.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 81.1-a over \(\Q(\sqrt{14}) \)

Isogeny class 81.1-a contains 4 curves linked by isogenies of degrees dividing 14.

Curve label	Weierstrass Coefficients
81.1-a1	\( \bigl[a + 1\) , \( a\) , \( 0\) , \( 15 a - 27\) , \( 46 a - 142\bigr] \)
81.1-a2	\( \bigl[a + 1\) , \( a\) , \( a\) , \( -8 a - 34\) , \( -80 a - 303\bigr] \)
81.1-a3	\( \bigl[a + 1\) , \( a\) , \( 0\) , \( 195 a - 702\) , \( 2674 a - 9979\bigr] \)
81.1-a4	\( \bigl[a + 1\) , \( a\) , \( a\) , \( -188 a - 709\) , \( -3383 a - 12660\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrr} 1 & 7 & 2 & 14 \\ 7 & 1 & 14 & 2 \\ 2 & 14 & 1 & 7 \\ 14 & 2 & 7 & 1 \end{array}\right)\)

Isogeny graph