Elliptic curve isogeny class 46.2-b over number field \(\Q(\sqrt{2}) \)

• Base field: \(\Q(\sqrt{2}) \)
• Label: 2.2.8.1-46.2-b
• Conductor: 46.2
• Rank: \( 0 \)

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

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

Elliptic curves in class 46.2-b over \(\Q(\sqrt{2}) \)

Isogeny class 46.2-b contains 2 curves linked by isogenies of degree 11.

Curve label	Weierstrass Coefficients
46.2-b1	\( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( 946 a - 1473\) , \( 20242 a - 29187\bigr] \)
46.2-b2	\( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( a - 3\) , \( -2 a + 3\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 11 \\ 11 & 1 \end{array}\right)\)

Isogeny graph