Elliptic curve isogeny class 3.1-b over number field \(\Q(\sqrt{22}) \)

• Base field: \(\Q(\sqrt{22}) \)
• Label: 2.2.88.1-3.1-b
• Conductor: 3.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 3.1-b over \(\Q(\sqrt{22}) \)

Isogeny class 3.1-b contains 2 curves linked by isogenies of degree 7.

Curve label	Weierstrass Coefficients
3.1-b1	\( \bigl[a + 1\) , \( -1\) , \( 1\) , \( 3043 a - 14259\) , \( -201370 a + 944522\bigr] \)
3.1-b2	\( \bigl[a + 1\) , \( -1\) , \( a + 1\) , \( a - 4\) , \( 2 a - 4\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph