Elliptic curve isogeny class 4802.1-bd over number field \(\Q(\sqrt{2}) \)

• Base field: \(\Q(\sqrt{2}) \)
• Label: 2.2.8.1-4802.1-bd
• Conductor: 4802.1
• Rank: \( 1 \)

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

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

Rank

Rank: \( 1 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

Elliptic curves in class 4802.1-bd over \(\Q(\sqrt{2}) \)

Isogeny class 4802.1-bd contains 2 curves linked by isogenies of degree 3.

Curve label	Weierstrass Coefficients
4802.1-bd1	\( \bigl[a + 1\) , \( 0\) , \( a\) , \( 75 a - 207\) , \( 217 a + 2431\bigr] \)
4802.1-bd2	\( \bigl[a + 1\) , \( 0\) , \( a\) , \( 5 a + 3\) , \( -35 a - 47\bigr] \)