Elliptic curve isogeny class 112.1-a over number field \(\Q(\sqrt{14}) \)

• Base field: \(\Q(\sqrt{14}) \)
• Label: 2.2.56.1-112.1-a
• Conductor: 112.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 112.1-a over \(\Q(\sqrt{14}) \)

Isogeny class 112.1-a contains 6 curves linked by isogenies of degrees dividing 18.

Curve label	Weierstrass Coefficients
112.1-a1	\( \bigl[a\) , \( 0\) , \( a\) , \( -685\) , \( -7674\bigr] \)
112.1-a2	\( \bigl[a\) , \( 0\) , \( a\) , \( -5\) , \( -2\bigr] \)
112.1-a3	\( \bigl[a\) , \( 0\) , \( a\) , \( 15\) , \( -30\bigr] \)
112.1-a4	\( \bigl[a\) , \( 0\) , \( a\) , \( -145\) , \( -702\bigr] \)
112.1-a5	\( \bigl[a\) , \( 0\) , \( a\) , \( -45\) , \( 54\bigr] \)
112.1-a6	\( \bigl[a\) , \( 0\) , \( a\) , \( -10925\) , \( -452090\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 9 & 3 & 6 & 18 & 2 \\ 9 & 1 & 3 & 6 & 2 & 18 \\ 3 & 3 & 1 & 2 & 6 & 6 \\ 6 & 6 & 2 & 1 & 3 & 3 \\ 18 & 2 & 6 & 3 & 1 & 9 \\ 2 & 18 & 6 & 3 & 9 & 1 \end{array}\right)\)

Isogeny graph