Elliptic curve isogeny class 22.1-b over number field \(\Q(\sqrt{14}) \)

• Base field: \(\Q(\sqrt{14}) \)
• Label: 2.2.56.1-22.1-b
• Conductor: 22.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 22.1-b over \(\Q(\sqrt{14}) \)

Isogeny class 22.1-b contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
22.1-b1	\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( 3 a + 3\) , \( 3 a + 7\bigr] \)
22.1-b2	\( \bigl[a + 1\) , \( a - 1\) , \( a\) , \( 13 a - 47\) , \( 35 a - 131\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph