Elliptic curve isogeny class 2025.1-d over number field \(\Q(\sqrt{2}) \)

• Base field: \(\Q(\sqrt{2}) \)
• Label: 2.2.8.1-2025.1-d
• Conductor: 2025.1
• Rank: \( 2 \)

Base field \(\Q(\sqrt{2}) \)

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

Elliptic curves in class 2025.1-d over \(\Q(\sqrt{2}) \)

Isogeny class 2025.1-d contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
2025.1-d1	\( \bigl[a\) , \( 1\) , \( 1\) , \( -5 a - 6\) , \( -4 a - 6\bigr] \)
2025.1-d2	\( \bigl[a\) , \( 1\) , \( a + 1\) , \( -11 a - 16\) , \( 17 a + 24\bigr] \)

Rank

Rank: \( 2 \)

Isogeny matrix

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

Isogeny graph