Elliptic curve isogeny class 22.2-b over number field \(\Q(\sqrt{23}) \)

• Base field: \(\Q(\sqrt{23}) \)
• Label: 2.2.92.1-22.2-b
• Conductor: 22.2
• Rank: \( 1 \)

Base field \(\Q(\sqrt{23}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 23 \); class number \(1\).

Elliptic curves in class 22.2-b over \(\Q(\sqrt{23}) \)

Isogeny class 22.2-b contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
22.2-b1	\( \bigl[1\) , \( 0\) , \( a\) , \( -273 a - 1307\) , \( 5340 a + 25604\bigr] \)
22.2-b2	\( \bigl[1\) , \( 0\) , \( a\) , \( -3 a - 12\) , \( 11 a + 47\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph