Elliptic curve isogeny class 144.1-a over number field \(\Q(\sqrt{22}) \)

• Base field: \(\Q(\sqrt{22}) \)
• Label: 2.2.88.1-144.1-a
• Conductor: 144.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 144.1-a over \(\Q(\sqrt{22}) \)

Isogeny class 144.1-a contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
144.1-a1	\( \bigl[a\) , \( 1\) , \( 0\) , \( 168 a + 802\) , \( 420 a + 1980\bigr] \)
144.1-a2	\( \bigl[a\) , \( 1\) , \( 0\) , \( -42 a - 183\) , \( -84 a - 384\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph