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

• Base field: \(\Q(\sqrt{38}) \)
• Label: 2.2.152.1-22.2-d
• Conductor: 22.2
• Rank: \( 1 \)

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

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

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

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

Curve label	Weierstrass Coefficients
22.2-d1	\( \bigl[1\) , \( -1\) , \( 0\) , \( -5 a + 31\) , \( 6 a - 37\bigr] \)
22.2-d2	\( \bigl[1\) , \( -1\) , \( 0\) , \( 470 a - 2899\) , \( -13901 a + 85693\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph