Elliptic curve isogeny class 4761.1-d over number field \(\Q(\sqrt{2}) \)

• Base field: \(\Q(\sqrt{2}) \)
• Label: 2.2.8.1-4761.1-d
• Conductor: 4761.1
• Rank: \( 0 \)

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

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

Elliptic curves in class 4761.1-d over \(\Q(\sqrt{2}) \)

Isogeny class 4761.1-d contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
4761.1-d1	\( \bigl[a\) , \( a\) , \( 1\) , \( -20 a - 29\) , \( -64 a - 91\bigr] \)
4761.1-d2	\( \bigl[a\) , \( -a - 1\) , \( 1\) , \( -22 a - 32\) , \( 77 a + 109\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph