Elliptic curve isogeny class 14.2-a over number field \(\Q(\sqrt{22}) \)

• Base field: \(\Q(\sqrt{22}) \)
• Label: 2.2.88.1-14.2-a
• Conductor: 14.2
• Rank: \( 1 \)

Base field \(\Q(\sqrt{22}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 22 \); class number \(1\).

Elliptic curves in class 14.2-a over \(\Q(\sqrt{22}) \)

Isogeny class 14.2-a contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
14.2-a1	\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( -75 a - 348\) , \( 527 a + 2471\bigr] \)
14.2-a2	\( \bigl[a + 1\) , \( a - 1\) , \( 1\) , \( 5 a + 27\) , \( 14 a + 65\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph