Elliptic curve isogeny class 14.1-b over number field \(\Q(\sqrt{22}) \)

• Base field: \(\Q(\sqrt{22}) \)
• Label: 2.2.88.1-14.1-b
• Conductor: 14.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 14.1-b over \(\Q(\sqrt{22}) \)

Isogeny class 14.1-b contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
14.1-b1	\( \bigl[1\) , \( 0\) , \( a + 1\) , \( -640 a - 3000\) , \( 19709 a + 92440\bigr] \)
14.1-b2	\( \bigl[1\) , \( 0\) , \( a + 1\) , \( 3220 a + 15105\) , \( 56342 a + 264264\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph