Elliptic curve isogeny class 46.1-b over number field \(\Q(\sqrt{2}, \sqrt{3})\)

• Base field: \(\Q(\sqrt{2}, \sqrt{3})\)
• Label: 4.4.2304.1-46.1-b
• Conductor: 46.1
• Rank: \( 0 \)

Base field \(\Q(\sqrt{2}, \sqrt{3})\)

Generator \(a\), with minimal polynomial \( x^{4} - 4 x^{2} + 1 \); class number \(1\).

Elliptic curves in class 46.1-b over \(\Q(\sqrt{2}, \sqrt{3})\)

Isogeny class 46.1-b contains 2 curves linked by isogenies of degree 11.

Curve label	Weierstrass Coefficients
46.1-b1	\( \bigl[a^{2} + a - 1\) , \( -a^{2} - a + 1\) , \( a^{2} - 2\) , \( 120 a^{3} - 476 a^{2} + 182 a - 67\) , \( 4490 a^{3} - 10669 a^{2} + 16 a + 1270\bigr] \)
46.1-b2	\( \bigl[a\) , \( -a^{2} - a + 2\) , \( a^{3} - 4 a + 1\) , \( a^{3} - 3 a + 2\) , \( 3 a^{3} + 7 a^{2} + a - 3\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

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

Isogeny graph