Elliptic curve isogeny class 162.1-b over number field \(\Q(\sqrt{14}) \)

• Base field: \(\Q(\sqrt{14}) \)
• Label: 2.2.56.1-162.1-b
• Conductor: 162.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 162.1-b over \(\Q(\sqrt{14}) \)

Isogeny class 162.1-b contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
162.1-b1	\( \bigl[a + 1\) , \( a\) , \( a\) , \( 16 a + 56\) , \( 1068 a + 3992\bigr] \)
162.1-b2	\( \bigl[a + 1\) , \( a\) , \( a\) , \( -704 a - 2644\) , \( 17088 a + 63932\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph