Elliptic curve isogeny class 25.1-b over number field \(\Q(\sqrt{10}) \)

• Base field: \(\Q(\sqrt{10}) \)
• Label: 2.2.40.1-25.1-b
• Conductor: 25.1
• Rank: \( 0 \)

Base field \(\Q(\sqrt{10}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 10 \); class number \(2\).

Elliptic curves in class 25.1-b over \(\Q(\sqrt{10}) \)

Isogeny class 25.1-b contains 2 curves linked by isogenies of degree 5.

Curve label	Weierstrass Coefficients
25.1-b1	\( \bigl[a\) , \( 1\) , \( 1\) , \( -238 a - 748\) , \( -3825 a - 12096\bigr] \)
25.1-b2	\( \bigl[a\) , \( 1\) , \( 1\) , \( 2 a + 12\) , \( 4 a + 14\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph