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

• Base field: \(\Q(\sqrt{2}) \)
• Label: 2.2.8.1-4802.1-bg
• 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-bg over \(\Q(\sqrt{2}) \)

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

Curve label	Weierstrass Coefficients
4802.1-bg1	\( \bigl[a + 1\) , \( -a\) , \( a\) , \( -76 a - 207\) , \( -217 a + 2431\bigr] \)
4802.1-bg2	\( \bigl[a + 1\) , \( -a\) , \( a\) , \( -6 a + 3\) , \( 35 a - 47\bigr] \)