Elliptic curve isogeny class 63.1-a over number field \(\Q(\sqrt{14}) \)

• Base field: \(\Q(\sqrt{14}) \)
• Label: 2.2.56.1-63.1-a
• Conductor: 63.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 63.1-a over \(\Q(\sqrt{14}) \)

Isogeny class 63.1-a contains 6 curves linked by isogenies of degrees dividing 8.

Curve label	Weierstrass Coefficients
63.1-a1	\( \bigl[1\) , \( a - 1\) , \( 1\) , \( 4082 a - 15271\) , \( -776251 a + 2904466\bigr] \)
63.1-a2	\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( 118 a + 444\) , \( 119 a + 446\bigr] \)
63.1-a3	\( \bigl[1\) , \( a - 1\) , \( 1\) , \( 482 a - 1801\) , \( -3115 a + 11656\bigr] \)
63.1-a4	\( \bigl[1\) , \( a - 1\) , \( 1\) , \( 4682 a - 17516\) , \( 328321 a - 1228464\bigr] \)
63.1-a5	\( \bigl[1\) , \( a - 1\) , \( 1\) , \( 5882 a - 22006\) , \( -483175 a + 1807876\bigr] \)
63.1-a6	\( \bigl[1\) , \( -a - 1\) , \( 1\) , \( -94082 a - 352021\) , \( 30525859 a + 114217306\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 8 & 2 & 4 \\ 8 & 1 & 2 & 4 & 4 & 8 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 8 & 4 & 2 & 1 & 4 & 8 \\ 2 & 4 & 2 & 4 & 1 & 2 \\ 4 & 8 & 4 & 8 & 2 & 1 \end{array}\right)\)

Isogeny graph