Elliptic curve isogeny class 34.1-b over number field \(\Q(\sqrt{38}) \)

• Base field: \(\Q(\sqrt{38}) \)
• Label: 2.2.152.1-34.1-b
• Conductor: 34.1
• Rank: \( 1 \)

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

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

Elliptic curves in class 34.1-b over \(\Q(\sqrt{38}) \)

Isogeny class 34.1-b contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
34.1-b1	\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -4 a + 8\) , \( -5 a + 21\bigr] \)
34.1-b2	\( \bigl[a + 1\) , \( -a - 1\) , \( a + 1\) , \( -4 a - 2\) , \( -a - 7\bigr] \)

Rank

Rank: \( 1 \)

Isogeny matrix

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

Isogeny graph