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

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

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

Curve label	Weierstrass Coefficients
4802.1-w1	\( \bigl[1\) , \( a + 1\) , \( a\) , \( 1503 a - 2458\) , \( 48068 a - 51240\bigr] \)
4802.1-w2	\( \bigl[1\) , \( a + 1\) , \( a\) , \( 33 a - 8\) , \( -148 a - 378\bigr] \)