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

• Base field: \(\Q(\sqrt{14}) \)
• Label: 2.2.56.1-22.1-a
• 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-a over \(\Q(\sqrt{14}) \)

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

Curve label	Weierstrass Coefficients
22.1-a1	\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -28 a - 98\) , \( -2405 a - 8994\bigr] \)
22.1-a2	\( \bigl[a + 1\) , \( -a\) , \( a + 1\) , \( -1538 a - 5748\) , \( -63797 a - 238702\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph