Elliptic curve isogeny class 49.1-a over number field \(\Q(\sqrt{14}) \)

• Base field: \(\Q(\sqrt{14}) \)
• Label: 2.2.56.1-49.1-a
• Conductor: 49.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 49.1-a over \(\Q(\sqrt{14}) \)

Isogeny class 49.1-a contains 4 curves linked by isogenies of degrees dividing 14.

Curve label	Weierstrass Coefficients
49.1-a1	\( \bigl[1\) , \( -1\) , \( 0\) , \( -2\) , \( -1\bigr] \)
49.1-a2	\( \bigl[1\) , \( -1\) , \( a\) , \( 262 a - 982\) , \( -5572 a + 20845\bigr] \)
49.1-a3	\( \bigl[1\) , \( -1\) , \( 0\) , \( -37\) , \( -78\bigr] \)
49.1-a4	\( \bigl[1\) , \( -1\) , \( a\) , \( -4463 a - 16697\) , \( 314979 a + 1178540\bigr] \)

Rank

Rank: \( 1 \)

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