Elliptic curve isogeny class 22.2-b over number field \(\Q(\sqrt{38}) \)

• Base field: \(\Q(\sqrt{38}) \)
• Label: 2.2.152.1-22.2-b
• Conductor: 22.2
• Rank: \( 0 \)

Base field \(\Q(\sqrt{38}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 38 \); class number \(1\).

Elliptic curves in class 22.2-b over \(\Q(\sqrt{38}) \)

Isogeny class 22.2-b contains 2 curves linked by isogenies of degree 5.

Curve label	Weierstrass Coefficients
22.2-b1	\( \bigl[a + 1\) , \( a\) , \( a\) , \( 5 a + 15\) , \( 3 a + 9\bigr] \)
22.2-b2	\( \bigl[a + 1\) , \( a\) , \( a\) , \( -840 a - 5195\) , \( -38810 a - 239251\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph